Lampard scored a club record 211 goals in 648 Chelsea appearances over 13 years, playing in tandem with defender Terry as the Blues won every major club trophy.
"The GREATEST player in the history of our great football club," Terry wrote on Instagram.
"All the great memories together winning trophy after trophy year after year I will never forget
You have won everything and should be extremely proud.
"It's been my pleasure and honour to play and experience all those great moments with you.
"A gentleman both on and off the pitch, leader in the dressing room and if I could choose one person next to me in the trenches it would be you.
"A great dad to your two beautiful girls and I'm proud to call you my mate.
"Good Luck for the future, whatever you choose to do will be a huge success
Love Ya Lampsy.
"LEGEND HERO INSPIRATION + THE BEST EVER."
Lampard joined Chelsea in 2001 and left in June 2014 after a stellar career shared with Terry.
The 36-year-old defender described the dedication which marked Lampard's career.
"The best trainer by a million miles every single day, inspiring me and everyone at the club," Terry added.
"I miss you next to me in the dressing room and miss you grabbing a bag of balls after training when everyone went inside.
"You stayed out working on your finishing, 20 goals a year wasn't good enough for you, every year you wanted 25,30 goals.
"I love that about you
I will miss you getting 4 cones and doing sprints after training - setting the example for the kids in the academy."
Striker Didier Drogba, who combined with Lampard and Terry in an imposing spine of Chelsea's first Premier League-winning team, added his tribute
Drogba wrote on Instagram: "A Gentleman with true values I've been honored to play and spend so many years next to him.
"I've learnt so much at practices with you but even more when we were staying after training trying to find ways to score more goals!!!
"I could continue writing to tell all the stories, the goals the fun the difficult moments we shared but I'm just gonna say Thank you LEGEND."
Source : PA