The band have been lined up to play a headline set at Glastonbury in June followed by their own show in London's Hyde Park in July, according to The Sun.
"It was the reunion many thought would never happen. Graham [Coxon] and Damon [Albarn]’s relationship had become toxic by 2002," a source told the newspaper.
"But they’ve patched up their differences and are friends again.
"The group have done some rehearsals and are all chuffed with the results. They’ve decided now is the time to go back out on the road."
Albarn last month confirmed that the band would return to the studio in 2009, five years after releasing their last album Think Tank.