The company wants to roll out Leapingsalmon.com's hand-prepared meal-kits to a number of stores, and continue its online ordering service.
Thresher said the deal made sense because the two companies had much in common, especially since Leapingsalmon.com had added wine to its deliveries.
Thresher Group chief executive David Williams said it was too early to say which off-licence chains in its portfolio would incorporate Leapingsalmon.com services.
But he added: "We work hard at tailoring our offer to various customer groups, as we have demonstrated recently with a new shop format designed for the stylish singles' market.
"The stylish singles' market is perfectly suited to the Leapingsalmon offer."
The five Leapingsalmon railway kiosks remain outside the Thresher deal. They were bought by rival Rocket in May.