Graham Potter’s side agreed a £53m deal for the Frenchman in December but there were fears that a failure to finish in the top-four would see Nkunku change his mind on a move to Stamford Bridge.
Despite spending £600m since Todd Boehly took charge just nine months ago, Chelsea are outsiders for Champions League qualification.
Nkunku has emerged as one of Europe’s most promising playmakers during his time with Leipzig, who he joined from boyhood club Paris Saint-Germain in 2019.
But, despite interest from PSG, Manchester United and Liverpool, Chelsea have won the race to sign Nkunku.
The Frenchman completed medical checks with the club at the end of 2022 and Fabrizio Romano says the playmaker has now signed his Chelsea contract.
Nkunku will officially become a Chelsea player at the start of July and Potter will hope that he forms a crucial part of a new-look forward line.