Having initially named a 26-strong provisional party on May 17, Hodgson had to whittle the squad down by three ahead of Tuesday’s Uefa deadline.
Manchester City’s Fabian Delph had already dropped out due to a groin complaint, with the Football Association confirming on Tuesday that Newcastle winger Townsend and Leicester midfielder Drinkwater had not made the 23-man squad.
Hodgson’s decision means England will have three goalkeepers, seven defenders, eight midfielders and five forwards in France - a group including teenage sensation Rashford.
Just three months after making his first appearance for United, the 18-year-old has won the FA Cup, signed a new contract and earned a place at Euro 2016.
Rashford impressed the England coaching staff by following up impressive training displays with a dream international debut, netting 138 seconds into the 2-1 win against Australia on Friday.
That display ratcheted up the pressure on Daniel Sturridge, but he too got the nod despite being the only member of the squad not to appear in either of the preparation matches.
The 26-year-old was absent for the victory against Turkey due to the Europa League final and was ruled out of the Socceroos clash with a calf strain.
Sturridge made a timely return to training on Monday, though, and has been selected ahead of Townsend and Drinkwater.
The latter had made the first of three England appearances in March, but there was no place for the Leicester midfielder in the 23-man squad.
Reacting to the news via his Instagram account, Drinkwater said: “Disappointed not to make the final 23! Would of been a fantastic experience to go to the euros as a player... But I’ll be supporting the country like I always have!
“The seasons been a huge positive for me.. Going into next season as a premier league champion! Good luck to the lads... Bring it home #england”
Jordan Henderson and Jack Wilshere returning to fitness was key to Drinkwater’s absence, with the pair handed the number 14 and 18 shirts respectively for Euro 2016.
Sturridge has been given number 15 and Rashford will wear 22, while Harry Kane, Wayne Rooney Jamie Vardy take up shirts nine, 10 and 11.
Tottenham pair Kyle Walker and Danny Rose have been given the number two and three shirts ahead of full-back rivals Nathaniel Clyne and Ryan Bertrand.
England welcome Portugal to Wembley on Thursday in their final preparation match before Euro 2016.
Hodgson’s men begin Group B against Russia on June 11 in Marseille, before taking on Wales in Lens on June 16 and travelling to St Etienne on June 20 to face Slovakia.
JOE HART (Manchester City, 19/04/87, 58 caps, 0 goals)
England’s established number one and an experienced campaigner, Hart has been at the sharp end for club and country for several years. Will be asked to lead and organise.
FRASER FORSTER (Southampton, 17/03/88, 6 caps, 0 goals)
Returned from 10 months out injured to set a new club record of six straight clean sheets earlier this season. A fantastic goalkeeper and more than able deputy.
TOM HEATON (Burnley, 15/04/86, 1 caps, 0 goals)
Named in the Championship team of the season after his consistently solid performances helped the Clarets win the title. Made debut against Australia as thanks for his work as third-choice goalkeeper
NATHANIEL CLYNE (Liverpool, 05/04/91, 12 caps, 0 goals)
Now fully settled into life at Jurgen Klopp’s Liverpool, he brings energy to everything he does from right-back and caught the eye in the friendly win over Germany.
KYLE WALKER (Tottenham, 28/05/90, 15 caps, 0 goals)
Has flourished under Mauricio Pochettino at Spurs and will be battling Clyne for a starting spot despite featuring in just one of the qualifiers.
DANNY ROSE (Tottenham, 02/07/90, 3 caps, 0 goals)
Has timed his run perfectly having only made his senior bow in March, but Rose’s showings against Germany and Turkey make a compelling case for him to start the tournament at left-back.
GARY CAHILL (Chelsea, 19/12/85, 42 caps, 3 goals)
A figure of some seniority now, Cahill’s experience is valued by Hodgson, who will be hoping the centre-half will be not be adversely affected by Chelsea’s dire season or the recent injections in his hip.
CHRIS SMALLING (Man Utd, 22/11/89, 24 caps, 0 goals)
The post-Ferguson years have not been kind to many at Old Trafford, but Smalling’s authority and consistency have risen and he is rapidly building his international credentials. Captained the country for the first time against Australia.
RYAN BERTRAND (Southampton, 05/08/89, 8 caps, 0 goals)
Still lacking meaningful international experience almost four years after his debut, but continues to impress with Saints and earns his spot in what has become a crowded field at left-back.
JOHN STONES (Everton, 28/05/94), 10 caps, 0 goals)
Still regularly linked with £40million transfers to the Champions League elite but dropped by a struggling Everton side earlier in the campaign. Question marks over his confidence, if not his talent, yet remains a big part of the future.
DELE ALLI (Tottenham, 11/04/96, 7 caps, 1 goal)
The PFA Young Player of the Year and a driving force behind Spurs’ title push, Alli’s versatility and range of skills means England’s main dilemma will be how to get the most from him.
JORDAN HENDERSON (Liverpool, 17/06/90), 25 caps, 0 goals)
A badly-timed knee injury left the midfielder sweating over his place but proved his fitness by featuring both warm-up friendlies. His work-rate is an important asset.
JAMES MILNER (Liverpool, 04/01/86, 59 caps, 1 goal)
The well-travelled 30-year-old has already hinted he will consider his international future after the tournament, but for now he adds an experienced head to the more dynamic talents around him and can contribute a leadership role even without starting.
ERIC DIER (Tottenham, 15/01/94, 6 caps, 1 goal)
A revelatory showing at the base of the midfield in the 3-2 friendly win over Germany, when he also opened his goalscoring account, made him a lock-in. Offers defensive nous and comfort on the ball in that role and versatility across the back four. The own goal against Australia looked an aberration.
ADAM LALLANA (Liverpool, 10/05/88, 22 caps, 0 goals)
A regular fixture in the Roy Hodgson era, but still awaiting his defining moment for the Three Lions. Malleable enough to succeed in a variety of positions and systems, but may have to make the most of limited opportunities.
ROSS BARKLEY (Everton, 05/12/93, 22 caps, 2 goals)
Has had his best season in terms of goals but few would argue Barkley’s progress has been serene. A victim, perhaps, of Everton’s downward trajectory and Hodgson will hope a change of scenery brings out the best in one of his most skilful players.
JACK WILSHERE (Arsenal, 01/01/92, 30 caps, 2 goals)
Another season of injury woe for the 24-year-old, but his bad luck ceased in time for him to get back on the pitch before the end of the campaign. Hodgson is a huge admirer of the elegant midfielder and considers him worth a fitness gamble, especially having featured in both warm-up friendlies.
RAHEEM STERLING (Man City, 08/12/94, 22 caps, 2 goals)
His big money move to the Etihad Stadium has not been a roaring success so far and there is a concerning inconsistency in his game. But he has pace, tricks and unpredictability in his favour and netted twice in qualifying.
WAYNE ROONEY (C) (Man Utd, 24/10/85, 110 caps, 52 goals)
Captain. Record goalscorer. Most decorated player in the squad. What more is there to say about Wayne Rooney? Quite a lot, as it turns out. A star in qualifying but outperformed over the past season by a handful of strikers and debate rages as to how best he can now be used, despite scoring against Australia.
HARRY KANE (Tottenham, 28/07/93, 11 caps, 5 goals)
Has now enjoyed two barnstorming seasons in the Premier League and is the home-grown symbol of Spurs’ compelling rebirth. Has carried that confidence into the early part of his international career and looks England’s most obvious goal threat, underlined by netting minutes into the Turkey win.
JAMIE VARDY (Leicester, 11/01/87, 7 caps, 3 goals)
The more he terrorises defences with his fast, direct runs and tops up his goal tally with a sniper’s precision, the harder it is to believe he ever had to rise so far through the ranks. Having netted in three successive international matches, England will look to harness his hunger.
DANIEL STURRIDGE (Liverpool, 01/09/89, 17 caps, 5 goals)
Injury problems meant he slipped off England’s radar for the best part of 18 months but while he may not possess the sharpest all-round game he is an instinctive goalscorer. A calf strain had raised questions about his place, but Hodgson has plumped for the oft-injured striker.
MARCUS RASHFORD (Man Utd, 31/10/97, 1 cap, 1 goal)
In the space of 92 days, the precocious 18-year-old made his Manchester United debut, won the FA Cup and scored on his international debut. There is a fearlessness and verve about Rashford, with his displays on international duty enough to see him head to France.