The country's largest household supplier said it was to phase them out as part of a number of "big steps" aimed at transforming the market to give customers a "fairer, simpler deal and lower bills".
It announced the shift as the Government moves to introduce price caps on SVTs - a default tariff that has no end date and is currently used by 50% of UK homes.
The charges have been described by the Prime Minister as a "rip-off" with a recent inquiry by a regulator finding UK households were over-paying by an estimated £1.4bn annually.
British Gas currently has five million SVT customers on its books.
It said it was to remove tariffs without an end date to new customers from the spring - offering a series of fixed deals instead.