The increases will take effect on March 31, two years after the last increase in stamp prices.
The now-privatised Royal Mail said it had "thought carefully" about the impact on customers and its business before making the decision.
Stephen Agar, Royal Mail's managing director of consumer and network access, said: "We understand that nobody likes to pay more, especially in the current economic climate. Our prices remain amongst the best value for money in Europe, and we have the highest service specification of any major European country."
Royal Mail said that, under the regulatory framework, it could have increased second class stamps to 57p, adding that its prices were among the best value in Europe, where the average for a first class letter is 67p and 60p for second class.
A large letter first class stamp up to 100g will rise by 3p to 93p, while a large second class stamp will go up by 4p to 73p.