It employs more than 200 people and has annual revenues of £180m.
Rivalling Dixons
"Dabs is a dotcom success story and one of the best companies in its field," said BT Retail chief executive Ian Livingston.
BT's push into online retailing will place it in direct competition with Dixons, whose owner DSG International announced earlier this month that it would disappear from the High Street to trade exclusively online.
"Dabs.com's outstanding expertise will boost BT's online power to sell innovative, value-for-money, communication and converged IT products and offer great service to a wide range of customers," added Mr Livingston.
"This purchase strengthens our online IT and digital products sales and service presence for small and medium-sized businesses as well as for consumer customers."