The Posh record appearance holder passed away earlier this afternoon (October 8).
He had recently been diagnosed with motor neurone disease and was given the freedom of the city this year.
Tommy made 482 league and 77 cup appearances from the left wing, scoring 128 goals, in a career that also saw him appear for Northampton Town, Newcastle and Chelsea.
In 2008, Robson became the first ever inductee to the Peterborough United Hall of Fame.
The club's official Twitter account described him as "the nicest man you will ever meet".
Posh owner Darragh MacAnthony said on Twitter: "So tragically sad to lose this legend
"Loved by all & Will be missed by us all. Tommy was heartbeat of our football club. Thoughts with his family"
Free Kicks Foundation said: "We are devastated to hear the news of Tommy’s passing. A friend, a gentleman who always had time for a chat and a laugh."