The high-rise estate in Swiss Cottage was the first to be found to be fitted with defective cladding following the Grenfell disaster.
Wates originally secured the recladding deal back in January 2019 but then failed to agree on final terms with the council 18 months later which saw the contract retendered.
It was split into four similar towers – now won by McLaren – and a separate £22m deal for the estate’s Blashford Tower which was was singled out because of its structural difference from the other blocks.
Graham was confirmed winner of the £22m single tower deal late last year.
McLaren will now start the pre-construction phase imminently because all the technical designs, surveys, and specifications have already been completed.
Work will start on site in early 2022 and the new cladding installation will begin in the summer as part of a schedule of works that will see the contractor working on two towers at the same time.
Councillor Meric Apak, Cabinet Member for Better Homes, said: “This is a significant step forward and I know that residents will be pleased to see this appointment as they share our determination to see works get underway as soon as possible.
“Our sights are now firmly set on quality and the safe completion and I look forward to a shared resident-focused approach as we move forward with the delivery of this project.”