Paulo Bernardo has completed his return to Celtic from Benfica on a five-year deal, worth £3.5m.
There was an option-to-buy clause on Bernardo's loan deal from last season, for a fee of around £6.5m, which Celtic have managed to negotiate down.
Bernardo, 22, has now become Brendan Rodgers' first outfield signing of the summer.
The midfielder spent last season on loan at the Scottish champions as they clinched a league and cup double.
Celtic have already secured two goalkeepers in Kasper Schmeichel and Viljami Sinisalo, with the club keen to secure a return for Norwich striker Adam Idah.
Bernardo: I love this club
Speaking to Celtic TV after rejoining Celtic on a permanent deal, Bernardo said: "It's amazing for me and it's a big step in my career.
"I really enjoyed last season when we won the championship and the cup, so it was great for me – my first two titles in my career, too.
"I love the club, I love the fans and I love the city, too, so it's very, very nice to be here again.
"I love the atmosphere at Celtic Park and away in all the games. Celtic is a big, big club. The fans feed us in the game so we can score one more goal or win the game in the last minute."
No transfer panic for Rodgers
Speaking prior to Bernardo's return, Brendan Rodgers told Sky Sports News there is "still work to do" in the transfer window but there is no need to panic:
"In transfers there are a lot of moving parts, it's never as easy as seeing a player and just bringing them in but we'd hope by the end of August that we would have the team supported who we want it.
"You cannot snooze in this game of football, you always have to be developing and improving. We want to ensure we have an improved squad for this season to take on all the challenges that we have.
"Everyone would love to get their work done as soon as they can. We would love to have had everything done for the first game of the season but that doesn't always end up being the case.
"My hope is we can be much stronger coming out of the August window than what we finished last season."
Celtic begin their title defence at home to Kilmarnock on Sunday, live on Sky Sports.
When does the summer transfer window open and close?
The 2024 summer transfer window is now open and will close on August 30 at 11pm UK time in England and at 11.30pm in Scotland.
The Premier League and Scottish Premiership brought forward Deadline Day to link up with the other major leagues in Europe. The closing dates were set following discussions with the leagues in England, Germany, Italy, Spain and France.