The deal, which is worth an initial €14m (£12.5m/$15.8m) deal sees Spanish forward Santi Mina move in the other direction, returning to his former club after four seasons away.Their agreement also includes the two-year loan of new Valencia signing Jorge Saenz, who recently arrived from Tenerife.
Maxi’s move brings to a close a summer of speculation for the Uruguayan, who was heavily linked with a switch to the Premier League with West Ham following the recent departure of Marko Arnautovic.
However, Sunday's news will see the 22-year-old remain in Spain’s top flight for the foreseeable future after two successful seasons with Celta, where he helped himself to 30 goals in 73 games across all competitions.
The Uruguay international originally arrived in Europe in 2017 having started his professional career with Montevideo-based Defensor Sporting in his home country.
A proposed move to West Ham reportedly collapsed earlier this month due to the €50m release clause in Maxi’s Celta Vigo contract.
La Liga rules meant that the sum had to be paid in full in order to take the forward to London – a condition that the Hammers were reluctant to agree to, with instalments their preferred method of payment.
And as the player himself explained to the club's official website, the prospect of Champions League football with Valencia also swayed his decision after their fourth-place league finish last season.
“I’m very happy to be joining Valencia,” said Maxi. “They’re a very big club and I’m happy to be here.
“It’s really nice to be able to play in the Champions League. I’ve never done that before, and from a young age I’ve always dreamt of playing in the Champions League and La Liga.
“I’m very grateful to Valencia and very happy. I came here with Celta and when we arrived at the stadium there were all the fans waiting for the Valencia players. It was a really beautiful thing.
“I want to help the team and score many goals. I hope that good things are on the way. I’m going to give my all, as I have done for every club for which I’ve played.
“I was able to meet some of my teammates the other day, although a lot of them were missing still.
“I’m very eager to stat training and give everything for Valencia.”