Gundogan, 32, has agreed a two-year deal with Barca with an option for a third year, turning down an offer to extend his seven-season stay at City as well as proposals from Premier League side Arsenal and clubs in Saudi Arabia, sources said.
The deal is pending the results of a physical, which Gundogan underwent on Wednesday, sources said.
Barcelona's ongoing financial issues meant they explored the free agent market, and in March ESPN revealed that Barca were in talks with the Germany international.
Sources told ESPN that City were unwilling to match Barca's financial offer, and would only extend a contract for one year with an option for a second.
Andreas Christensen and Franck Kessie both arrived on free transfers last summer, while sources have told ESPN that defender Inigo Martinez is also set to join Barca following the expiry of his contract with Athletic Club this month.
Barca value the former Borussia Dortmund player's versatility in the middle of the pitch, particularly his ability to operate in a deeper role -- although sources have said the club would still prefer to bring in a direct replacement for the departing Sergio Busquets.
Gundogan is calling time on his spell at City after captaining the English side to a historic treble, culminating in their first Champions League trophy earlier this month.
The midfielder scored 11 goals in 51 appearances this season, including a brace in the FA Cup final against Manchester United. He leaves City after winning five Premier League titles and 14 trophies in total.