The deal, agreed on Sunday via video conference, is the largest cut in oil production ever to have been agreed.
Opec+, made up of oil producers and allies including Russia, announced plans for the deal on 9 April, but Mexico resisted the cuts.
Opec has yet to announce the deal, but individual nations have confirmed it.
The only detail to have been confirmed so far is that 9.7 million barrels per day will be cut by Opec oil producers and allies.
On Monday in Asia, oil rose over $1 a barrel in early trading with global benchmark Brent up 3.9% to $32.71 a barrel and US grade West Texas Intermediate up 6.1% to $24.15 a barrel.
Shares in Australia jumped 3.46% led by energy exporters, but Japan's Nikkei 225 fell 1.35% on continued concerns of poor global demand because of the spread of the coronavirus.
"This is an unprecedented agreement because it's not just between Opec and Opec+... but also the largest supplier in the world which is the US as well as other G-20 countries which have agreed to support the agreement both in reducing production and also in using up some of the surface supply by putting it into storage," Sandy Fielden, director of Oil Research at research firm Morningstar, told the BBC.
US President Donald Trump and Kuwait's energy minister Dr Khaled Ali Mohammed al-Fadhel tweeted the news, while Saudi Arabia's energy ministry and Russia's state news agency Tass both separately confirmed the deal on Sunday.