Retail fuels Europe rally; DAX ends sharply up

European equities closed sharply higher on Tuesday, with a surge in retail stocks (STOXX:.SXRP) helping to boost investor sentiment. The pan-European FTSEurofirst 300 (FTSE International: .FTEU3) closed around 1.3 percent higher, with German stocks (^GDAXI) ending 1.6 percent up. The French CAC (Euronext Paris: .FCHI) closed 1.4 percent higher, while Portuguese stocks (Euronext Lisbon: .PSI20) soared to end over 2 percent higher.

Among U.K. retailers, WM Morrison (London Stock Exchange: MRW-GB) surged to close around 4.5 percent higher after the announcement that CEO Dalton Philips would leave the firm.

Read More Morrisons CEO to leave after Christmas sales fall London's FTSE 100 (FTSE International: .FTSE), in which the supermarket chain features, ended unofficially 0.7 percent higher.

Meanwhile, shares in U.K. online retailer ASOS (London Stock Exchange: ASC-GB) rose as much as 9 percent after it posted a 15 percent rise in Christmas sales.

Debenhams (London Stock Exchange: DEB-GB) was the major laggard for the sector, with shares falling as much as 8 percent after its trading update highlighted a slight dip in sales over the last 19 weeks. Markets had opened in negative territory, with investors continuing to fret about the falling price of oil.

Oil prices slumped more than 5 percent overnight , extending the second-deepest rout on record, after Goldman Sachs slashed its short-term price forecasts and Gulf producers showed no sign of curbing output. Heavily-weighted stocks like BP (London Stock Exchange: BP.-GB), Total (Euronext Paris: FP-FR) and Shell (London Stock Exchange: RDSA-GB) fell in early deals but staged a turnaround in later in the day.

U.S. stocks rallied on Tuesday, with equities bouncing back after a two-session drop, after aluminum-producer Alcoa kicked off the fourth-quarter earnings season by beating estimates. Meanwhile, the rate of inflation in the U.K. fell to 0.5 percent in December year-on-year , according to new data on Tuesday morning. This was its lowest level in 14 years.

Asian shares were mixed on Tuesday , as traders weighed a better-than-expected trade report from the Chinese mainland and the continued fall in global oil markets. Follow us on Twitter: @CNBCWorld