Mancini has been widely linked with a move for Dzeko, 24, since the summer, and the player is understood to have written a letter to City last month expressing his desire to move to Eastlands.
Mancini has now confirmed the two clubs have reached an agreement, with City set to pay Wolfsburg £27 million.
"We have agreed a fee," he said. "He is a good player and all the teams in Europe want him, but we have an important game at Arsenal coming up and I will speak about him after that."
City face a tough task at Arsenal on Wednesday as both David Silva and Mario Balotelli have been ruled out through injury.
"It is a big problem," Mancini said. "Neither of them will be available. David has been an important player for us and has been doing well recently. Hopefully, he will be back for the Wolves game on January 15.
"Mario might be back for the FA Cup tie at Leicester on Sunday."
A victory at Emirates Stadium would only heighten the belief that City can be serious challengers for the title this season, but Mancini has been keen to play down their prospects.
"Arsenal, Chelsea, United and Tottenham all have more experience than us," he said. "Probably one of those four teams will win the title.
"We just want to work, so we can improve and try to keep getting better."
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