Benchmark crude for December delivery was up $1.95 at $92.15 a barrel at afternoon Singapore time in electronic trading on the New York Mercantile Exchange. The contract fell $2.97, or 3.2 percent, to settle at $90.20 in New York on Wednesday.
Brent crude was up $1.27 at $110.18 a barrel on the ICE Futures Exchange in London.
After a meeting that began Wednesday, EU President Herman Van Rompuy said early Thursday that policymakers struck a deal that will reduce Greece's debt to 120 percent of its GDP in 2020. The plan will require banks to take on 50 percent losses on their Greek bond holdings.
Van Rompuy also said the eurozone and International Monetary Fund will give Greece another euro100 billion ($140 billion).
Investors cheered the accord as a first step toward containing Europe's sovereign debt crisis. The Dow Jones industrial average gained 1.4 percent on Wednesday and stock markets in Asia rose Thursday.
"This could be a turning point for the eurozone debt crisis," said analyst Victor Shum of energy consultancy Purvin & Gertz in Singapore. "It's a significant development that private investors have agreed to take a 50 percent haircut on Greece."
Crude has jumped about 21 percent from $75 on Oct. 4 amid growing investor optimism that the U.S. economy will avoid a recession this year. Shum said he expects oil to trade near $100 by the end of the year.
In other Nymex trading, heating oil rose 0.4 cents to $3.06 per gallon and gasoline futures gained 3.9 cents at $2.66 per gallon. Natural gas fell 1.2 cents at $3.58 per 1,000 cubic feet.