In late London trade Brent North Sea crude for January delivery was up usd 3.71 at USD 50.09, the first time it has risen above USD 50 in a month. West Texas Intermediate was up USD 3.85 at USD 49.08.
The accord announced by the Organization of the Petroleum Exporting Countries is aimed at reducing a global supply glut that has kept prices painfully low.
It represents a dramatic reversal from OPEC's Saudi-led strategy, introduced in 2014, of flooding the market to pressure rivals, in particular US shale oil producers.
The cartel will lower its monthly output by 1.2 million barrels per day (bpd) to 32.5 million bpd from January 1, Qatar's energy minister and president of the OPEC conference said.
"This is a major step forward and we think this is a historic agreement, which will definitely help rebalance the market and reduce the stock overhang," Mohammed Bin Saleh Al-Sada told a news conference.
He also said that the deal will help global inflation accelerate to a "more healthy rate", including in the United States.
According to an OPEC statement, Saudi Arabia will reduce output by 486,000 bpd from October levels to 10.1 million bpd. Iraq will cut by 210,000 bpd to 4.4 million bpd and UAE 139,000 to 2.9 million bpd.
It finalises a preliminary deal struck in September in Algeria when OPEC agreed to cut production but left the details to clear up later.
Negotiations got bogged down in a game of poker between OPEC's three biggest producers, Saudi Arabia, Iraq and Iran, on who would do the heavy lifting.
Iraq had said it was short of money to fight Islamic State group extremists, while Iran wants to hike output to levels before it was hit by Western sanctions over its now-reduced nuclear programme.
The dispute was complicated by the fierce rivalry between Shiite Iran and Sunni Saudi Arabia, backing different sides in the wars in Yemen and Syria.
Iran will actually increase production by 90,000 bpd to 3.8 million bpd under the deal. Oil Minister Bijan Namdar Zanganeh flashed a victory sign to reporters as he left OPEC headquarters.
Libya and Nigeria are exempted, while Indonesia has suspended its membership.