Designed by architect SimpsonHaugh, each building will provide 490 private flats for sale as well as a residents’ lounge and gym.
The uppermost levels of each tower will contain eight three-bed duplex penthouses.
Located near Deansgate at the southern end of the city centre, the twin buildings will be styled with chamfered edges.
According to Renaker’s viability report, the project will cost around £329m to build.
It is Renaker’s second major skyscraper scheme to get the planning go-ahead this year.
Last month the Manchester builder and developer gained planning for four towers ranging from 39 to 60 storeys at Trinity Islands in Deansgate.
Also designed by SimpsonHaugh, this scheme would create nearly 2,000 flats, varying from one, two and three bedrooms.
Trinity Islands is expected to cost around £530m to build.