The midfielder, who is in Miami with England's World Cup squad, has been linked with a move to new MLS franchise New York City FC and reportedly held exploratory talks with them over the weekend.
Lampard spent 13 seasons at Chelsea and made 648 appearances, becoming the club's leading goalscorer with 211 goals.
During his time at Stamford Bridge, he won the Premier League on three occasions to go with four FA Cups, two League Cups, a Champions League title and one Europa League.
In a statement, Lampard said: "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.
"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 club will move forward, and as a Chelsea man I have no doubt that with the quality of the players that are there, they will continue with the success that we have all enjoyed over the past seasons.
"Finally and most importantly, I would like to thank the Chelsea fans. I believe they are the greatest fans in world football. 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.
"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.
"Whatever the next challenge is for me I will always be amongst you and have Chelsea in my home and in my heart. Hopefully I will get to see you all soon to say goodbye properly. In the meantime thank you for the memories and keep making history!"
Chelsea detailed Lampard's "momentous career" on their official website and described him as "one of the very greatest players to have represented the club".
The tribute piece continued: "Any Chelsea supporter who has had the good fortune to watch Super Frank Lampard in full flow will know we have never seen his like in our midfield before, and we will be very blessed to again see his equal."