New York's main contract, light sweet crude for delivery in September, surged $1.53 to $97.23 per barrel. Brent North Sea crude gained $1.25 to $117.99.
"What we are seeing is a relief rally in the oil markets... It is really due to the deal in the US regarding raising the debt ceiling," said Victor Shum, senior principal of Purvin and Gertz energy consultants in Singapore.
US President Barack Obama announced last night an 11th-hour deal to avert a potentially catastrophic debt default for the United States, the world's richest country and biggest oil consumer.
The deal would raise the country's $14.3 trillion debt ceiling by about $2.4 trillion in two steps, while calling for roughly the same about in spending cuts over 10 years.
In the US Congress, leaders of the Democratic-held Senate and the Republican-led House of Representatives said they would present the framework to their rank-and-file today ahead of final votes to approve the deal.
All eyes will now be turned to Congress, which will have to approve the deal before midnight tomorrow (0930 IST Wednesday) to prevent the default.
Crude markets were depressed last week as the August 2 deadline for reaching a compromise debt deal loomed.
A default by the United States would send shudders through the global economy that could lead to another financial crisis.