The pan-European FTSEurofirst 300 Index provisionally closed higher by 1.2 percent at 1,352.06 points on Tuesday.
Late during the day, Siemens announced it was ready to make an offer for France's Alstom, so long as the latter granted it access to company data and permission to interview management to enable due diligence. Shares in Siemens closed higher by 0.6 percent; trade in Alstom shares is suspended until Wednesday.
Read MoreSiemens will make an offer to Alstom
Meanwhile, Nokia shares rose 2.9 percent after the company reported a promising profit rise in its networks business—now the core part of its business, following the sale of its handset unit to Microsoft.
Deutsche Bank, one of Germany's largest financial corporations, announced a better-than-expected first-quarter net profit of 1.08 billion euros ($1.5 billion) on Tuesday, as its core fixed income business slumped by less than expected; shares rose by 2.2 percent.
Oil giant BP announced it is hiking its dividend after announcing a fall in profit in the first quarter fall due to higher costs in searching for oil. Shares closed higher by 2.9 percent.
Meanwhile, shares in Peugeot Citroen closed higher by around 10 percent after the French carmaker launched the second part of a 3 billion euro ($4.2 billion) capital increase to fund its recovery plan and deal with China's Dongfeng.
U.S. stocks also climbed on Tuesday, after a round of first quarter earnings from companies including Dow-listed Merck.
Merck posted earnings that topped estimates, but the drug manufacturer's revenue came in just under expectations. Its results came a day after Britain's Reckitt Benckiser confirmed it was in talks to acquire Merck's consumer health business for nearly $14 billion.
Earnings season has been "not that bad and not that good," commented Peter Cardillo, chief market economist at Rockwell Global Capital, on Tuesday.
Individual stocks news managed to outweigh concerns over Ukraine and weaker-than-expected growth data in the U.K. on Tuesday. Official data showed U.K. first quarter growth came in slightly less than forecast at 0.8 percent.
Elsewhere, data showed unemployment in Spain fell slightly this month. The figure came in at 25.9 percent, down from March's 26.0 percent, but above market expectations.
The European Commission also published its economic sentiment index for March, which showed a slip in the euro area but a rise in the European Union as a whole.