The changes will come into effect on 11 July 2018 and will affect 2.36mln customers of SSE Energy Services and M&S Energy.
The FTSE 100-listed firm said gas price will go up 5.7%, and electricity price will go up 7.7%, meaning a typical dual fuel customer will see a rise of around £1.50 each week, or £76 per year.
The company said customers who are on fixed-price tariffs, have a prepayment meter, or on the vulnerable customer safeguard tariff will not be affected.
SSE Energy services will also be removing its £6 per fuel, per year paperless billing discount from 11 July.
Stephen Forbes, chief commercial officer of SSE, said the company "deeply regret having to raise prices.”
“However, as we’ve seen with recent adjustments to Ofgem’s price caps, the cost of supplying energy is increasing, and this ultimately impacts the prices we’re able to offer customers,” Forbes said.
SSE is the last of the “big six” energy companies to increase prices.
Meanwhile, EDF Energy will increase its electricity prices by an average of 2.7% from 7 June, and Npower will raise energy prices by £64 a year from 17 June.