Reports emerging in the early hours of the morning in Germany say the Bosnian’s transfer has been agreed.
Džeko has started from the bench in 14 of his 28 league appearances this season, managing 12 goals, and has supposedly become frustrated with his role at the club.
The 27-year-old moved to City in 2011 from German club Wolfsburg for £27 million but has failed to hold down a regular place in Roberto Mancini’s starting XI.
The news of Džeko’s move to Dortmund will cast further doubt over the future of Robert Lewandowski, who scored all four of Dortmund’s goals against Real Madrid in the Champions League semi-final first leg last week.
The Polish striker has already confirmed he will not be signing another contract at the 2011 and 2012 Bundesliga champions with a move to Bayern Munich being heavily touted.
Džeko is expected to leave as part of a massive summer overhaul as City look to win back the Premier League title after losing it to neighbours Manchester United this year.