The 36-year old was released from the Blues after 717 first team appearances.
Terry had attracted interest from Bournemouth, West Bromwich Albion and Swansea.
Explaining his decision, Terry said: "For me it was just the mental side of playing against Chelsea, it was just too much to get over for me.
"I was 22 years at the football club, 22 unbelievable years, I'm very proud of that but this is a new chapter in my life, my career.
"I wish Chelsea well next season and will be watching out but my thoughts are 100 per cent here."