According to transfer specialist Fabrizio Romano, the two clubs have agreed on a deal worth 22 million euros, with a further nine million euros available through performance-related bonuses.
The add-ons are expected to be linked to appearances and Barcelona's success in domestic and European competitions.
Adeyemi is set to sign a contract until 2031 after deciding not to extend his stay at Borussia Dortmund. With just one year remaining on his current deal, the Bundesliga club opted to cash in on the 24-year-old this summer.
The winger joined Dortmund from RB Salzburg in 2022 in a deal worth 30 million euros and has established himself as one of the club's quickest attacking players.
Sky Germany reported that Adeyemi will earn around six million euros per season at Barcelona, while Dortmund have also negotiated a 35 per cent sell-on clause as part of the agreement.
Joao Cancelo has returned to Barcelona with the Portugal international making clear that he was prepared to sacrifice both playing time and part of his salary to make the move happen.
Borussia Dortmund have completed the signing of Greek attacking midfielder Giannis Konstantelias from PAOK, with the 23-year-old committing his future to the Bundesliga club on a long-term contract.
Bayern Munich are hopeful Jamal Musiala will be fit for the start of the new season after the Germany international recovered from a worrying collapse during Saturday's 3-1 pre-season victory over RB Leipzig.
Cristian Romero has confirmed his departure from Tottenham Hotspur as he prepares to join Atletico Madrid after five years in north London.
