The decision will see prison officers receive a 1.7 percent rise, while police will get a 1 percent increase plus a 1 percent bonus for the year.
The announcement comes amid reports of mass strikes over pay condition, with Unite leader Len McCluskey suggesting he would even support illegal action.
Confirming the increase, Treasury Minister Liz Truss said hard-working public sector workers deserved to be "fairly rewarded".
But the move has been slated by TUC general secretary Frances O'Grady, who branded the "below inflation" offer "pathetic".
Widespread dissatisfaction with the long-running squeeze on household incomes has been cited by politicians from both major parties as a key factor in the Tories disastrous election result in June.
This has led to growing calls from across the political spectrum for the Government to abandon the 1 percent cap, which has led to real-terms pay cuts of up to Â£3 an hour for some sectors.
Over the summer, ministers repeatedly stressed that the Government has learnt the lesson of the election and was "listening" to concerns around issues like income.
However, they also highlighted the Treasury's determination to balance the books, and indicated no decision would be made before the Autumn Budget.
At this morning's Cabinet meeting, ministers approved recommendations by independent pay bodies to increase wages for prison officers in order to tackle shortages of staff and expertise.
Confirming the decision, a Downing Street spokesman told reporters: "Cabinet agreed that public sector workers are among the most talented and hard-working people in our society. They, like everyone else, deserve to have fulfilling jobs that are properly rewarded."
The spokesman went on to hint that other sectors could also see their pay increase over the coming year.
"There will still be a need for pay discipline over coming years to ensure the affordability of public services and the sustainability of public sector employment. However, the Government recognises that in some parts of the public sector, particularly in areas of skill shortage, more flexibility may be required," they said.
The announcement coincides with the latest inflation figures, which show rates have risen to 2.9 percent.
It also comes as union bosses raise the possibility of coordinated public sector strike action - even if they do not secure the legal requirement of a 50 percent turnout in the ballot.
Reacting to the increase, Steve White, chairman of the Police Federation of England and Wales, warned it will leave many officers "angry and deflated".
He said: "Police officers do not join the service to make huge amounts of money, they do it out of a sense of duty and this year in particular have been tested to the max. However, they expect to be paid suitably for the immensely demanding role they perform and this simply is not the case."
Ms O'Grady said: said: "This below-inflation pay offer is pathetic. Public sector workers have suffered seven long years of real pay cuts, and are thousands of pounds worse off.
"Today's announcement means bills will continue to rise faster than their wages. If ministers think a derisory rise like this will deal with the staffing crisis in our public services, they are sorely mistaken."
Liberal Democrat leader Sir Vince Cable said: "It is good to see the Government finally recognise that the public sector pay cap is no longer sustainable. The cap must now be lifted across the board so all public sector workers are given the pay rise they deserve."
more to follow