The Nigeria international had attracted interest from a number of clubs this summer but he was left out of City's pre-season tour of the United States in July as Leicester emerged as front-runners to land his signature.
The principles of the £25m deal have been in place for some time but the move was held up due to an image rights issue between Iheanacho and his former agents.
The striker will now have a medical in the East Midlands on Tuesday and the move is set to be completed this week.
City have insisted on a buy-back clause in the deal and it has been reported that the Etihad Stadium outfit will be able to re-sign the striker for a fee of around £35m.
Iheanacho emerged onto the scene under Manuel Pellegrini during the 2015-16 season but struggled for regular playing time under Pep Guardiola last term.
Guardiola made it clear to Iheanacho that he would have to find a new club at the beginning of the summer as City aim to recoup at least £100m in player sales this summer.
Midfielder Fernando is also on the verge of a move away from the Etihad, with Galatasaray heavily linked.
The sales of Iheanacho and Fernando will take the total amount of players sold by City this summer from around £30m to over £60m. Nolito, Enes Unal, Aaron Mooy and Aleksandar Kolarov have all been sold so far, while Fabian Delph is thought to be close to a move to Stoke City.
Buyers are yet to be found for Samir Nasri, Eliaquim Mangala, Wilfried Bony and Jason Denayer.
The Blues have already spent in excess of £200m this summer and they remain determined to bring in at least one new forward and a centre-back.
The Gunners have made it clear publicly that Alexis is not for sale and though they have been just as stubborn in private, City officials still hope to sign him this summer. However, the possibility of waiting a year and bringing him in on a free has also recently been discussed.
City have also been in contact with Monaco over 18-year-old forward Kylian Mbappe, and though reports have insisted the club are not willing to pay fees in the region of £150m, they have been interested in the Frenchman for over a year and are exploring the possibility of reaching an agreement this summer in the face of interest from Real Madrid.
The Blues also want to sign a centre-back, with Real Sociedad's Inigo Martinez a target. The Spain international has a £26.5m buy-out clause and could emerge as a viable option for Guardiola, despite having previously been low down the City boss' list of targets as moves for Virgil van Dijk, Leonardo Bonucci and other, more senior defenders were explored.
Holger Badstuber has also been discussed by Guardiola and his coaching staff in recent weeks but City's interest is not thought to be concrete. Indeed, reports in Germany on Tuesday suggest the Germany international is close to joining Stuttgart on a free transfer.
Tosin Adarabioyo, the 19-year-old central defender who signed a contract extension earlier this summer, is set to go out on loan.