The England international had been in discussions with officials from Stamford Bridge for the past two weeks.
No fee has been revealed, although it is believed that Chelsea will pay Wanderers around £7m for Cahill's signature.
"Chelsea is a massive club, it is a club that looks to win trophies season in season out and it is a big opportunity for me to be a part of that," the 26-year-old told the club's official website. "Opportunities like this you can't turn down."
Cahill will wear the number 24 shirt at Stamford Bridge.