The 29-year-old playmaker has signed a three-year contract with the club owned by Russian billionaire Roman Abramovich, winners of the last two Premier League titles, Chelsea said on their website.
Ballack is expected to be rotated in Chelsea's teams on domestic and European duty with Ghana's Michael Essien in a three-man midfield featuring top goalscorer Frank Lampard and Frenchman Claude Makelele in the holding role.
Ballack will start his career in English football after helping Bayern win consecutive German league and cup doubles, part of a six-trophy haul during four years at the club.