Sidwell turned down a new contract with Reading despite helping the club finish eighth in its first ever Premier League season.
Chelsea said he passed a medical exam Tuesday.
The Blues need backup in midfield this season as several players will be taking part in the Jan. 20-Feb. 10 African Cup of Nations - notably Ghana's Michael Essien and Nigeria's John Obi Mikel.
Sidwell was a trainee with Arsenal, and was loaned to Brentford, Beveren and Brighton before he joined Reading in 2003. He helped the club get promoted to the Premier League in 2006.