Gundogan is believed to have been offered a three-year deal by Barcelona and is expected to complete his move to the Spanish champions when his City contract expires at the end of June.
City were reported to have been willing to give their 32-year-old captain a new one-year contract with the option of a further 12 months.
But Gundogan's impending move to the Camp Nou was revealed on the same day City agreed a £30 million ($38 million) deal to sign Chelsea midfielder Mateo Kovacic.
Kovacic's versatility and experience would help compensate for the loss of the influential Gundogan, whose leadership and knack for scoring crucial goals played a key role in City's success in Pep Guardiola's reign.
Gundogan netted twice in City's FA Cup final victory over Manchester United this season before Guardiola's Premier League champions went on to beat Inter Milan in the Champions League final.
The Germany international played 51 games this term, scoring 11 goals including six in his last seven appearances during the tense treble run-in.
City are only the second English side to win all three major trophies in a single season.
Gundogan will be fondly remembered by City fans as one of the understated touchstones of their club's golden era.
The former Borussia Dortmund midfielder has won five Premier League titles, two FA Cups, four League Cups and the Champions League in his seven years at City.
Guardiola was keen to keep Gundogan, who has a close relationship with the City boss after living in the same luxury Manchester apartment block for many years.
But, given Gundogan's age, City reportedly did not want to match Barcelona's offer and appear to have taken a pragmatic decision to let him leave.
