Germany's DAX index finished up 36.06 points, or 0.9%, to 4,061.13. Traders were ignoring the ZEW institutional investor and analyst sentiment survey, which fell to 49.7 in April - the lowest level since July - from 57.6 in March. DaimlerChrysler, Siemens, and SAP were higher.
In Paris, the CAC 40 index moved 30 points higher, or 0.8%, to 3,773.43. Television Francaise 1 was higher after reporting higher first quarter ad revenue.
Asian markets finished mixed on Tuesday. In Japan, the Nikkei 225 index finished 188.05 points higher, or 1.6%, to close at 11,952.26. Banks rebounded from their sharp falls on Monday, and tech stocks benefited from the rises in U.S. tech stocks overnight.
In Hong Kong, the Hang Seng index lost 55.63 points, or 0.45%, to close at 12,394.37.