Lampard had reportedly been offered a new deal on reduced terms by Chelsea, but he has opted to bring an end to his 13-year spell with the Premier League team. (Agencies)
Several reports earlier on Monday claimed Lampard's representative has held talks with New York City over a prospective move to Major League Soccer's new franchise next March.
At least 10 other clubs, including newly-promoted QPR, are believed to have registered their interest in signing the star.
Lampard scored 211 goals in 649 appearances for the Blues, making him the club's all-time record goal-scorer.
He admitted it was a wrench to leave Chelsea after so many happy memories and he paid tribute to former chairman Ken Bates, who was in charge when he was signed from West Ham in 2001, and current owner Roman Abramovich, whose huge cash injection transformed the team into a European superpower.
"When I arrived at this fantastic club 13 years ago I would never have believed that I would be fortunate enough to play so many games and enjoy sharing in so much success," Lampard said in a statement released by his agent.
"This club has become part of my life and I have so many people to thank for the opportunity. Firstly, Ken Bates, who put his neck on the line to sign me as a young player and without him I would not have even begun this experience.
"Roman Abramovich, the man who saved our club and took us all to new levels. His desire to push the club to the top of the football world has rubbed off on everyone.
"All the managers and coaches who have helped me develop my game during the time I have been here. I have learnt from every one of them.
"All the brilliant team-mates who I have been lucky enough to train and play alongside for so long. Not just their football qualities but also the friendships I have gained along the way.
"I'd also like to give a special mention to all the staff and people behind the scenes at the club who do not receive the glory but without them the club would simply not function."
The 35-year-old's long and successful stay in west London has left him well established as a Chelsea legend after winning three Premier League titles, the Champions League, the Europa League, four FA Cups and two League Cups.
Despite his age, Lampard remained a key member of Jose Mourinho's squad this season and made 40 appearances, scoring eight goals in all competitions.
He is currently in Miami with the England squad preparing for friendlies against Ecuador and Honduras ahead of their World Cup campaign in Brazil and it is believed he will wait until after the tournament to decide his future.
Lampard's exit is likely to signal the end of an era for Chelsea, with long-serving left-back Ashley Cole also set to leave when his contract expires.
At the end of Chelsea's last home game of the season, a 0-0 draw with Norwich in May, Lampard stood in front of Chelsea's fans in the Matthew Harding Stand along Cole to take a last emotional bow.
Lampard, whose finest moment in a Chelsea shirt arguably came in 2012 when his superb display helped seal Champions League final victory over Bayern Munich in the German club's Allianz Arena, was quick to thank the Blues supporters.
"You have supported me from the moment I arrived. Not only on the pitch, but in difficult moments in my personal life off the pitch. I will never forget,” he said.
"I feel honoured to have shared so many special times with you. Bolton, Amsterdam, Munich, the list goes on and on. I, and we as a team, could not have achieved those moments without your support,” he added.
"Whatever the next challenge is for me I will always be amongst you and have Chelsea in my home and in my heart," Lampard said.
Lampard had reportedly been offered a new deal on reduced terms by Chelsea, but he has opted to bring an end to his 13-year spell with the Premier League team.