His former club said it was “devastated” to learn of his death.
Thompson, who retired in 2019, was diagnosed with cancer for a third time last year.
In its statement, Rochdale FC said he died “peacefully at home on Thursday, with his family by his side”.
He made over 200 appearances for Rochdale, who he joined from Manchester United‘s academy in 2005.
The club posted a tribute on X, describing the former midfielder as “a warm personality who had a deep connection with our club from a young age”.
In her tribute on Instagram, Thompson’s wife Chantelle said he had “made such an impact on so many people” and he was “the most incredible husband, son, brother, friend and father”.
During his career, he played for Tranmere Rovers, Bury and Carlisle United, with spells on loan at Wrexham and Southport.
He was first diagnosed with Hodgkin lymphoma in 2013, while playing for Tranmere.
When Thompson rejoined Rochdale from Carlisle in 2016 the disease soon returned, but he confirmed he was cancer free in June 2017.
Two years later, he announced his retirement at the age of 29, saying his body had been pushed “to the limit” having twice undergone treatment for cancer.
Last year, he revealed he had been diagnosed with stage four lymphoma which had spread to his lungs.
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Hodgkin lymphoma is a relatively aggressive type of cancer that can spread quickly through the body, according to the NHS.
Rochdale, who face Altrincham on Friday, have confirmed that players will wear black armbands during the National League match.
