Kessie, 25, arrives on a contract until June 2026 and a buyout clause of 500 million euros ($A760 million).

The move could accelerate Frenkie de Jong's speculated transfer to Manchester United.

Christensen comes after his contract with Chelsea ended. His deal is also until 2026 and contains the same buyout clause as Kessie's.

Kessie will be officially introduced on Wednesday. He will be the second Ivorian to play for Barcelona, after Yaya Toure in the late 2000s.

He has 58 international appearances and played at the Tokyo Olympics as Ivory Coast reached the quarterfinals.

The 26-year-old Christensen will be introduced on Thursday. He helped Chelsea win the Champions League, the Europa League and the Club World Cup, and was on the Danish national team that reached the semi-finals of the 2020 European Championship.

Kessie joined Milan on loan from Atalanta in 2017 and permanently signed with the club in 2019 for 33 million euros ($A50 million). He helped the rossoneri wn their first title in 11 seasons this year. In his six seasons with Atalanta and Milan, Kessie scored 45 goals.

Barcelona are reported to be in discussions with Manchester United about selling De Jong though president Joan Laporta said at the weekend Barca "have no intention of selling him, he wants to stay, we are happy to have him."

But Laporta added: "I'm going to do everything I can in my power so that Frenkie stays here, but there's also a salary issue and that would have to be adjusted."

Australian Associated Press