Finney died at the age of 91 on Friday having had a glittering career for both club and country. He scored 210 goals in 473 games for Preston and 30 in 76 England appearances.
Finney was renowned as one of the game’s great wingers and was famed for his double act in England colours with fellow wideman Sir Stanley Matthews.
“On behalf of The FA, I would like to send my deepest condolences to the family and friends of Sir Tom Finney,” Dyke said in a statement.
“He was one of English football’s all-time greats and will be much missed across the game. Sir Tom was a true one-club man at Preston North End and a fantastic player for England. He will rightly be forever remembered at Deepdale and Wembley.”
Finney spent his entire career at Preston after eschewing the chance for a lucrative move to Palermo and according to former North End team-mate Tommy Docherty, was as good as Lionel Messi.
“He was something else, the Lionel Messi of his day,” Docherty, who played with Finney between 1949 and 1958, told talkSPORT.
“He was a great person and a lovely man. I never heard him criticise anyone.”
Finney will be forever linked with Preston, his home-town club, and Docherty recalled how gates at Deepdale would be lower if Finney was not playing.
“If Tom was injured, they wouldn’t tell you the team at all,” he said. “If he was injured, and that was rare, there would be 20,000 at the game instead of 42,000.”
Docherty’s views were shared by former England captain Jimmy Armfield.
He told BBC Radio 5 Live: “He, in my opinion, is one of the really great footballers that this country has produced.
“As much as anything else, and it’s hard to explain to many people today, but it was the way he played and the way he carried himself - his whole demeanour of life. Really, Preston will be a very sad place.”
FIFA president Sepp Blatter also paid tribute, tweeting his own memories.
“Very sad news that Sir Tom Finney is no longer with us. Had privilege of watching @pnefc man play at 1954 WC,” he said.
Finney played in three World Cups in a career which, after being delayed by the Second World War, spanned from 1946-60 and was the first player to win two Footballer of the Year Awards.
Bill Shankly, the great Liverpool manager and a former Preston team-mate, once said: “Tom Finney would have been great in any team, in any match and in any age... even if he had been wearing an overcoat.”
Finney was nicknamed the ‘Preston Plumber’ during his career after his first trade, to which he returned and ran a successful business in after retiring from the game.
Additionally he worked in the media, was chairman of the Preston Health Authority and in 1998 was awarded a knighthood.
Preston announced the news in a brief statement on Friday night.
“Sir Tom was the greatest player to ever play for Preston North End and one of the all-time greats for England,” the statement read.
“The thoughts of everyone at the club, and those connected with it, are with his family at this time.”
Aside from a Second Division championship title, Finney never won any of the game’s major honours.
In 1954 the FA Cup final was billed to be his day - a year after his friend and rival Matthews inspired a famous Blackpool win - but Preston were beaten by West Brom.
Preston also finished First Division runner-up twice during his career.
Current club captain Kevin Davies tweeted: “Tonight we have lost a footballing Legend. A true gent and a loyal servant to his beloved PNE. RIP Sir Tom Finney.”
Finney remains joint sixth on England’s all-time goalscoring list.
Gary Lineker, the second-highest scorer with 48, tweeted: “Sir Tom Finney has left us. One of the greatest players this country has ever seen, and a true gentleman. #RIP.”
Football League Chairman Greg Clarke also added to the tributes, saying: “The Football League is deeply saddened to learn of Sir Tom’s death.
“He was quite possibly the finest player to have ever played in the Football League and was a true gentleman. He was also the epitome of the one-club man with few people ever having contributed as much to a single team, their city or our competition.
“He will be greatly missed by the English game.”
Former Republic of Ireland international Kevin Kilbane was also born in and played for Preston, and he tweeted: “I’m proud to say I grew up on the same street as Sir Tom Finney. Very sad to hear of his passing. #RIPSirTom #theprestonplumber.”
English champions Manchester United tweeted: “We’re saddened to hear of the passing of England and Preston North End legend Sir Tom Finney.”