Dzeko underwent a medical at Eastlands last night.
The Bosnia striker was due to arrive in Manchester earlier in the week after City agreed a fee with German club Wolfsburg last weekend.
But it is understood that a hitch in obtaining a visa put a spanner in the works and briefly put the deal on hold, says the Daily Mail.
At one point it is believed that Dzeko was stranded at Heathrow airport waiting for clearance to enter the country.
However, the 24-year-old finally reached Manchester last night and underwent initial medical examinations last night.
City boss Roberto Mancini hopes Dzeko will be available for selection ahead of the club's next league game at home to Wolves on January 15.