Recent data pointing to slowing global growth has fuelled hopes that policymakers in China, Europe and the United States will provide more stimulus to shore up sputtering economies.
Brent rose $3.34 to end at $100.68 a barrel, the highest settlement since May 31. Prices reached $101.58, the loftiest intraday price since front-month Brent reached $101.90 on June 11.
U.S. crude jumped $3.91 to settle at $87.66 a barrel, the highest close since May 30, after reaching $88.04 intraday.
Traders and analysts also pointed to short-covering ahead of the U.S. Independence Day holiday on Wednesday and said the strong rally had triggered buy-stop orders.
U.S. gasoline, up nearly 10 cents, and heating oil futures also rallied ahead of Wednesday's holiday.
Brent trading volume outpaced turnover for U.S. crude, with volume for both eclipsing their 30-day averages.
"The oil-price rally is motivated by growing expectation of monetary accommodation and also a return of Iran to the market's agenda," said Harry Tchilinguirian, head of commodity markets strategy at BNP Paribas in London.