The 35-year-old England international, Chelsea's all-time leading scorer with 211 goals, was out of contract.
Since joining from West Ham, Lampard had helped the club to three Premier League titles and the Champions League in 2012.
Lampard has yet to decide if he will retire, but has had offers from 16 other clubs.
The midfielder, who is currently with the England squad in Miami ahead of the World Cup, will not consider any of the offers until after the tournament finishes.
After joining from West Ham for £11m in June 2001, Lampard made 649 appearances for Chelsea, who also won four FA Cups, two League Cups and the Europa League in his time at the west London club.
