WTI Crude is now trading up 3.03 percent at $49.29 per barrel, with Brent Crude up 2.93 percent at $52.33 (1126GMT).
Prices slumped at the end of last week as a result of U.S. inventory data that was more bearish than expected, adding to the sense that Opec supply cuts are not enough to rebalance the market.
The global oil market is rebalancing and the pace at which supply and demand are falling into line is picking up, even if inventories still fail to reflect the impact of OPEC supply cuts, the International Energy Agency said on Tuesday. Surging U.S. production has raised concern that the Organization of Petroleum Exporting Countries and its partners are failing to reduce an oversupply.
"It seems more or less a slam dunk that there is going to be a continuation of the cuts", said Bjarne Schieldrop, chief commodities analyst at SEB Markets.
US bank Goldman Sachs said the deal "will likely further extend the oil price rebound. although the rally so far. has remained modest compared to the move that occurred a year ago when the OPEC cuts were first announced".
That is longer than the optional six-month extension specified in the deal, and shows that the battle to reduce overall supply has been more hard than originally anticipated, in part because of rising US production.
Instead of US crude oil inventories declining in the first quarter, they increased.
News of the joint deal sent crude prices up more than 1.5 percent in Asian trading.
The weak dollar and the deal extension will keep crude in current levels until there are signs that demand is still soft as per the weekly United States crude inventories to be released on Wednesday.
That is forcing Saudi Arabia and Russian Federation to step in again. That is longer than the optional six-month extension specified in the deal.
OPEC is set to convene on May 25 in a meeting where its members and Russian Federation are expected to roll over an agreement to cut production. The recent increase in Libyan output, together with a surge in North American shale production and signs of recovery in Nigeria, may undercut OPEC's strategy to re-balance the market and prop up prices.
Amid the cutbacks, production in the US, which isn't part of the agreement, has risen to the highest level since August 2015.
Oil prices rebounded strongly yesterday and were continuing to move higher this morning, after an extremely encouraging report on reserves in the US. They also come amid a market fallback in recent weeks over doubts that the cuts, which total some 1.8 million b/d from October levels, are effective, given stubbornly high stock levels and the resilience of U.S. shale.
"Russia and Saudi Arabia may be trying to coordinate a push to keep access to their most important market (China) in their favor and encourage Chinese importers to displace alternative cargoes", said Bell.
Still, energy analysts say the global oil demand outlook is positive.