The development, on the site of Biart Place, includes 100 new homes - 60 one and two-bedroomed apartments, 20 maisonettes and 20 two, three and four-bedroomed houses.
Construction company Willmott Dixon looks set to hand over the development's first phase of new homes to the council next month, with the first tenants set to move in soon after.
The council will allocate all homes at Navigation Way to eligible households registered on the council's housing waiting list.
Sustainable design and construction have been put at the heart of Navigation Way, with homes benefiting from electric vehicle charging points, solar panels and air source heat pumps.
The development has been backed by a £6.8 million grant from Homes England's Affordable Homes Programme 2021-2026, together with a further £2 million from the Government's Getting Building Fund.
Cllr Claire Edwards, Rugby Borough Council portfolio holder for communities and homes, regulation and safety, said: "The grant from Homes England has allowed us to allocate all homes at Navigation Way for social housing, which means every home will be allocated to eligible households registered on the council's housing waiting list.
"With the first phase of 51 modern, energy efficient homes set to be handed over to the council by Willmott Dixon next month, we're looking forward to welcoming the first tenants to Navigation Way in the autumn, the start of a new chapter for the former Biart Place site."
Councillors first approved plans to develop the site nearly seven years ago after structural surveys revealed both of Biart's tower blocks - which comprised 124 one and two-bedroomed flats - were beyond economic repair.
A year ago, councillors voted to name the new road serving the development Navigation Way to celebrate the role the railway and canal networks played in Rugby's rapid industrial growth in the 19th century.
The development's four apartment blocks were named Clayton House, Davenport House, Sherrard House and Lindon after pupils from Avon Park School were invited to suggest the names.
All four names were inspired by Rugby's iconic status as the birthplace of the game, with John Clayton, Alfred Davenport and Charles Sherrard all pupils at Rugby School who played for England against Scotland on 27 March 1871 - the first ever rugby international.
Lindon House commemorates the work of Rugby leathermaker Richard Lindon, who manufactured the first rugby footballs at his shop in Lawrence Sheriff Street.
Cllr Jerry Roodhouse, leader of Rugby Borough Council's Liberal Democrat group, said: "This project has come about thanks to the hard work of officers and a clear wish for the council to deliver council housing in Rugby.
"The development has been built to the latest energy standards. The task now is to work with our new tenants to ensure they are part of the community."
The second phase of homes at Navigation Way looks set to be handed over to the council in the new year.