Gallacher, 18, underwent a week-long trial at the Reds' Kirkby Academy earlier this month and impressed sufficiently to earn a permanent transfer to Anfield.
The young left-back is unlikely to be involved with the Reds' first team initially, with the club announcing that he will continue his development as part of the Under-23 squad.
Gallacher made 17 appearances for Falkirk this season and was welcomed to his new club by Kenny Dalglish.
"Liverpool FC can confirm the signing of Tony Gallacher from Falkirk in a permanent transfer, with the 18-year-old to join up with the Reds' development squad," the club said in a statement.
"Full-back Gallacher has put pen to paper on a contract to complete his move to Anfield."
Gallacher had drawn admiring glances from the likes of Barcelona, Manchester United, Rangers and Stoke City after breaking into Falkirk's first team at the age of 16 in 2015.
Falkirk manager Paul Hartley told the Scotsman: "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 becomes Liverpool's second signing of the January transfer window after the club struck a £75m deal to sign centre-back Virgil van Dijk from Southampton – a world-record fee for a defender.