The 18-year-old travelled south yesterday to complete a £200,000 switch to the Anfield giants following a successful trial earlier this month.
The left-back has been linked with interest from Barcelona, Manchester United, Rangers and Stoke City since breaking into the Bairns first-team in 2015 aged just 16.
But he will now try to follow in the footsteps of Scotland star Andy Robertson after Liverpool won the race for his signature.
Hartley said: “It’s an unbelievable move for Tony. For a player to come from Falkirk and go to Liverpool doesn’t happen a lot. It’s a dream come true, and we can’t stand in the way of that.
“Hopefully he goes there and proves how good a talent he is.
“There’s been a lot of transfer talk surrounding him over the last 18 months since he came into the team, but to go to Liverpool is a little but surreal for him. We wish him all the best. I’m sure he’s got a bright future ahead of him and it will be a dream come true.”
Gallacher has made 17 appearances for the Falkirk first team this season and will initially join up with Liverpool’s under-23s.
He is the latest to win a big move to English football from Falkirk, following in the footsteps of the likes of Scott Arfield, Murray Wallace, Stephen Kingsley, Jay Fulton, Ryan Blair and Botti Biabi in recent years.
Ironically, Gallacher’s move comes just weeks after Falkirk cut their ties with the Forth Valley Football Academy that helped develop the defender. And another Academy graduate, Cieran Dunne, could also win a transfer south after going on trial with Blackburn Rovers this week. The 17-year-old made his debut for the Bairns in October and has played six times.
Meanwhile, Ayr United manager Ian McCall is delighted to be working with Mark Kerr for a third time after recruiting the experienced midfielder on a deal until the end of the season.
The 35-year-old signed for the League 1 title hopefuls yesterday, just 24 hours after leaving Falkirk for a second time.
Kerr played under McCall at Falkirk before being signed by the same manager in 2003 when he was in charge of Dundee United.
The playmaker fell out of favour at Falkirk under Paul Hartley and a thrilled McCall said: “Mark is a boy I know really well having had him as a player at Falkirk and then signing him for Dundee United.
“The injuries that we have had have been no secret and we needed a holding midfield player.
“Mark might be 35 but he has always kept himself extremely fit, so there are no problems there.
“He is exactly the type of player you want for the run-in and he will be a big part of our squad.”
Wigan’s promotion push has been given a boost by the loan signing of Swansea midfielder Jay Fulton.
The 23-year-old, who has made 19 Premier League appearances for the Swans, has joined the Sky Bet League One leaders until the end of the season after passing a medical.
The former Falkirk player joins James Vaughan and Jamie Walker who also arrived at the DW Stadium this month.
Wigan boss Paul Cook said: “Jay will fit right in here. It is a good move for him and we are really looking forward to working with him and integrating him into our squad.”