Opec and non-member producers led by Russia agreed to a gradual increase in production for three months starting in January, ending a long annual meeting.
The group will bring 2 million barrels per day to the market, incrementally by 0.5 million bpd, starting in January.
The alliance, informally known as Opec+ will draw back 7.2 million bpd, reversing the 7.7 million bpd of curbs in place since August.
Opec+ also extended the period allowed for members to make compensatory cuts for earlier overproduction to the end of March.
The group, led by Saudi Arabia and Russia, will hold monthly ministerial meetings starting in January “to assess market conditions and decide on further production adjustments", Opec said in a communique.
"We actually had a very long discussion about the current state of the market and other factors, and we believe that today's market is rather stable, although there is still some uncertainty, of course,” Russian Deputy Prime Minister Alexander Novak said after the meeting.
“That is why, considering some stability, we have decided that we need to do this easing of cuts gradually, making a pause every month to review what's happening."
Mr Novak, who continues to handle Opec affairs after his promotion from energy minister to deputy premier, will visit Saudi Arabia in January to discuss issues relating to the market and bilateral relations.
Oil markets reacted positively to the news of Opec+ tapering cuts gradually.
Brent, the international benchmark, was up 1.24 per cent, trading at $48.85 per barrel at 12.04am UAE time on Friday.
West Texas Intermediate, which tracks US crude grades, was up 1.08 per cent, trading at $45.77 per barrel.
Saudi Energy Minister Prince Abdulaziz bin Salman, who this week tendered his resignation as chairman of the joint ministerial monitoring committee meeting, will now stay on, Opec said.
"I threw down the towel but the towel came back to me,” Prince Abdulaziz said.
He dismissed and criticised reports of a rift between producers.
"This is a grand commitment and this is a demonstration of responsibility by all participants,” Prince Abdulaziz said.
"This is a mature agreement and mature in the sense that the end of the day we all can agree by consensus."
Opec+ took into account the UAE’s concerns about the lack of compensation by other members of the alliance, he said.
“We’re given many assurances now," Prince Abdulaziz said.
"This is going to be a relentless quest and we’re going to make sure that everybody will discipline themselves as well as they can."
The group will continue to make exemptions for Libya, a key Opec producer, on humanitarian grounds.
The North African producer has taken 1.25 million bpd to the market since September, after it ended a 10-month force majeure.
“As an Opec member, usually when a country goes through a situation like this, we allow them to produce all the way to the last agreement that we had," Prince Abdulaziz said.