The 25-year-old was again an important player for his Italian club during the 2021-22 campaign, scoring seven goals and registering one assist in 39 appearances in all competitions.
A number of clubs had been linked with Kessie earlier this year, but there has not been any speculation in recent months, with Barcelona managing to come to an agreement with the Ivory Coast international.
"FC Barcelona and Franck Yannick Kessie have reached an agreement for the player to join Barça after the end of his contract with AC Milan," read a statement on the club's official website.
"The player will sign a contract until 30 June 2026 and his buy-out clause will be set at €500m (£429.8m)."
Barcelona have also revealed that Kessie will be presented as a Barcelona player on Wednesday, with the midfielder set to officially sign the contract before having pictures in the club's training kit.
There will then be a press conference in the afternoon, with the Ivorian set to answer questions for the first time since being confirmed as the club's latest acquisition.
Kessie leaves Milan with a record of 37 goals and 16 assists in 223 appearances for the San Siro giants, while he has also turned out for Cesena FC and Atalanta BC.
The midfielder has represented Ivory Coast on 58 occasions in all competitions, meanwhile, finding the back of the net six times for his national side.
"Franck Kessie is a player who contribute in attack and in defence. Capable of winning the ball back in midfield, the African midfielder also has impressive stats as a goalscorer, partly due to his ability to make runs into the penalty area," read a statement on Barcelona's official website.
Kessie's arrival could open the door for Barcelona to sell Frenkie de Jong, with the Netherlands international being strongly linked with a move to Manchester United.
Barcelona are working towards their pre-season opener against Olot on July 13, while they will start their 2022-23 La Liga campaign at home to Rayo Vallecano on August 13.
Despite their financial issues, the club are still working on a deal for Robert Lewandowski, although Bayern Munich are resisting the sale of the Poland international in the current market. body check tags ::