The smaller company's value, including Travis Perkins' offer for the equity, and BSS's debt and pension deficit is about £650m pounds, said TP chief executive, Geoff Cooper.
With earnings before interest, taxation and amortisation of £55m, Travis will pay 11.8 times EBITDA for BSS, he said.
"To have that multiple at the bottom of the cycle is a really good deal for our shareholders," he added.
Mr Cooper sought the opinion of Travis's top shareholders, who support the deal, he said. "That scale is going to be particularly important in the future, since all of us in the sector are looking to improve our buying performance and to do so requires scale."
The company, he explained, had not approached BSS before these discussions, which started about five or six weeks ago.
Mr Cooper could not say what the immediate cost savings might be or if sites would be closed or jobs cut.
The company could avoid store closures by shifting its eight brands between sites selling similar products, he said.
"On average, we close about half a dozen sites a year," Mr Cooper said. "We don't think that would be any different if we got this business in the group.
"The deal will probably receive anti-trust approval in the UK as there are enough independent stores and other suppliers to compete with a larger Travis Perkins," Mr Cooper said.