Customers will be able to chose whether to take advantage of the deal between 9am and 5pm on a Saturday or a Sunday, reports The Telegraph.
British Gas said consumers should see savings of about £60 a year.
But experts said it will not necessarily be the cheapest deal on the market, and advised people to shop around with other suppliers.
Most of British Gas’s 11 million customers will not be eligible, as only 2.4 million of these have smart meters.
For the first time, smart meters enable energy firms to work out the time of day when people are using power.
The move follows an announcement by British Gas in April that it had lost 224,000 customers in the first three months of 2016.
British Gas said the new FreeTime tariff will be the cheapest dual fuel deal on offer from the company.
But independent energy expert Ann Robinson said consumers might still find a lower tariff elsewhere.
“Consumers need to think about the small print, shop around and see if there’s a better deal out there,” she said.
However, she welcomed the innovative use of smart meters, saying people might be prepared to change habits to save money.
“It’s worth thinking about cooking your major roasts and stews, or doing two or three rounds of laundry on the same day,” she said.
Experts expect other suppliers to follow suit.
Large energy suppliers have now installed 2.75 million residential smart meters across the UK, less than 6% of all meters, according to the latest government figures.
In total, 53 million smart meters are due to be installed by 2020.
