The midfielder left Manchester City on a free transfer during the summer, joining the Spanish giants on a three-year deal after the Gunners failed with an offer to keep him in the Premier League.
Gundogan's final game for the club proved to be the Champions League final, which City won to claim a historic Treble, and the German says it was the perfect time to leave and fulfill a "childhood dream" of playing for Barcelona.
There were reports at the time that Gundogan was pushing for a longer contract which City were not offering - while both Barca and Arsenal were - but the player has denied those claims.
"I’m honest, and many people don’t know this, in the end, it wasn’t about a year or two," he told Bild.
"There was no problem with the running time. City waited a relatively long time until the talks really intensified. If this had happened a little earlier, the situation would have been different.
"So in the end it was the perfect ending, it couldn’t have come at a better time. It was also my childhood dream to play for FC Barcelona."