The former Beatle's band currently includes veteran American rockers Rick Derringer, Richard Page, Wally Palmar, Edgar Winter, Gary Wright and Gregg Bissonette.
The All-Starr Band will play Kiev Saturday, Moscow Monday and St. Petersburg Tuesday, RIA Novosti reports.
During the 15-nation tour, Starr will mark his 71st birthday July 7 with a concert in Hamburg, Germany, where the Beatles got their start 50 years ago.
Each set is to include songs by the Beatles, Starr and other band members.
This is the band's first European tour since 1999.