Watt, who famously scored in Celtic's 2-1 Champions League victory over Barcelona in 2012, flew out on Monday morning to finalise the move.
Watt spent last season on loan at Belgian side Lierse, scoring eight goals in 17 games, but he fell out with manager Stanley Menzo in March and was demoted to their 'B' squad.
He did not play for the club again, returning to Celtic at the end of the season.
The 20-year-old was involved in Celtic's pre-season training camp under new manager Ronny Deila but did not feature in either of the club's Champions League qualifiers against KR Reykjavik.
Watt posted on social media: "Delighted to sign a 5 year contract with Standard Liege today! Just want to thank everyone at Celtic for making my dreams come true and giving me an unforgettable 3 and a half years!
"It wasn't an easy decision to leave the club I support and I honestly can't explain the feeling I got every time I wore the hoops.
"And also a big thanks to the supporters who helped me during my Celtic career, i will never forget the atmosphere in most of the matches."
Having met Celtic's valuation of the player, Liege will be keen to complete the formalities of registering the striker for Wednesday's Champions League qualifier against Panathinaikos.
Watt made his debut for Scotland Under-21s in August 2012 in a friendly match against Belgium. He went on to make a total of nine appearances for the U21 side, scoring five times.
Deila insisted the deal suited both parties.
He said: "He wanted to go, he wanted the opportunity. It is a big club so I think it is a good move for him, to grow up as a person and develop as a player.
"You never know what is going to happen in the future. I hope he succeeds because he is a very nice boy but right now I think it was the right time to try something else."