The store will be located to the north of the proposed new £400m stadium and construction work starts this month.
McLaren was responsible for the successful delivery of Spurs new £45m state-of-the-art Training Centre in Enfield.
Paul Phillips, Project Director said: “We look forward to working with McLaren Construction, who have been a good partner during the construction of our new Training Centre.
“By appointing McLaren, we shall again be able to ensure that the new supermarket development is delivered in line with a strict contractor code of conduct similar to that which was employed in Enfield, and that our construction partners will take a responsible and sensitive approach to building within our community.”
Kevin Taylor, Chairman, McLaren Group said: “After the successful completion of the Club’s Training Centre, we are very proud to be awarded the contract for phase 1 of the development of the Club’s existing site.
“This award is testament to the strong partnership between McLaren and Tottenham Hotspur, and we look forward to continuing to build this relationship for the future.”
The new supermarket, which will be one of the largest of its kind in London, is 130, 000 sq ft with a sales floor area of 72,000 sq ft and will be operated by Sainsbury’s.
The development also includes 110,000 sq ft of commercial/educational space above the supermarket.