The company also said that it expects its residential gas prices to rise from the start of October, following a consultation process with the Commission for Energy Regulation.
Bord Gáis has 435,000 residential electricity customers.
'We recognise the strain that households are under at the moment and we have done our utmost to limit the overall price increase to 12% despite much higher increases in international wholesale prices,' said Jason Scagell, managing director of retail and trading, Bord Gáis Energy.
'The prices paid by Irish customers are intrinsically linked to international wholesale prices and with the markets signalling the prospect of higher winter prices, residential price increases have unfortunately become unavoidable.
'On this basis, we also expect that the Commission for Energy Regulation will approve price increases for residential gas customers from 1 October 2011, following a consultation which is due to commence shortly.'
Bord Gáis said that this was the first time that the company has increased prices since entering the residential electricity market in February 2009 and follows two successive cumulative price cuts of 15% in May and October 2009.
Wholesale electricity prices have increased 20% since Bord Gáis Energy last cut prices, the company said.
It said that the wholesale price of gas, used in the production of electricity, had increased 39% in the last year.
The average annual Bord Gáis residential electricity bill is €989 and gas bill is €689.
Customers who have difficulties paying their bills are being urged to get pay-as-you-go meters installed.
They cost €370 to install, but the energy board will provide them free of charge to those in serious arrears.
'We offer free pay-as-you-go meters to anyone who has entered into a repayment plan with us and is in arrears,' a spokesman said.
'The normal cost is €370.'