New York's main contract, light sweet crude for delivery in January, rallied $2.72 to $96.60 a barrel.
Brent North Sea crude for February jumped $2.70 to $106.34 in London afternoon deals.
"The softer US dollar supported the strong upside correction in the oil market," said Sucden Financial Research analyst Myrto Sokou.
The euro shot above $1.31 on Tuesday following positive German economic data. A weaker US unit makes dollar-denominated crude cheaper for buyers using the single currency, pushing up demand and in turn prices.
Oil climbed on Monday after recent losses as investors worried about North Korea after the death of leader Kim Jong-Il left the isolated communist nation in a state of uncertainty.
"Rising geopolitical tensions and fears of supply disruptions around the globe are likely to increase choppy crude trading next year," VTB Capital analyst Andrey Kryuchenkov said on Tuesday.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional