The other main rival buyer for the business, builders’ merchant Travis Perkins, is understood to have dropped out of the running over the weekend.
The French group, which owns Jewson and the Graham builders’ merchant chain, is also in talks to buy Wolseley’s French plumbing and heating business Brossette.
Together both deals are estimated to be worth £310m.
Ian Meakins, chief executive of Wolseley said: “The transactions we have announced today are the last significant disposals planned following last year’s strategic review.
“We will continue to focus and invest in our strongest businesses in core markets including building materials and wood solutions in France and plumbing, heating, pipe, climate and associated businesses in the UK.”
Long billed as the world’s largest plumbing and heating product supplier, Wolseley put the Build Center chain up for sale in May to concentrate on core business and pay down debts.
Build Center is ranked as the fourth largest builders’ merchant chain in the UK turning over £316m from around 200 outlets.
Saint Gobain will pay £145m for the business, which made a £4m trading profit in the 11 months to June.
Last month the US group sold its Electric Centers to Knutsford-based Edmundson Electrical.