Burrow won eight Super League titles, three World Club Challenges and two Challenge Cups during an iconic career with Leeds Rhinos.
He retired in 2017 but two years later it was revealed he had been diagnosed with motor neurone disease.
"It is with deep sadness that we announce the death of our beloved son, husband, father, brother and friend," a Leeds statement said on Sunday.
"Rob has always been a true inspiration throughout his life whether that was on the rugby league field or during his battle with MND (motor neurone disease).
"He never allowed others to define what he could achieve and believed in his own ability to do more."
Burrow made more than 400 appearances for Leeds between 2001 and 2017.
He raised millions of pounds to help build a new care centre for motor neurone disease patients alongside former team-mate Kevin Sinfield.
Burrow was made an MBE in the 2021 New Year Honours for his services to the sport and for his work in the motor neurone disease community.
"The outpouring of love and support that Rob and the whole Burrow family have received over the last four and a half years meant so much to Rob," Leeds added.
"In particular, the rugby league family and MND community have rallied around Rob to inspire him, thank you for your support.
"For those who knew Rob throughout his life, his determination and spirit in the face of MND over the last four and a half years came as no surprise."
