Bennett won silver alongside Kriss Akabusi, Garry Cook and Philip Brown in the 4x400m relay at the 1984 Games in Los Angeles.
The Southampton-born sprinter, who also won a silver medal in the world indoor championships in 1985 and was a twice European indoor champion, moved into coaching with UK Athletics following retirement.
Roger Black, who won Olympic silver in the 400m at Atlanta 1996, tweeted: "krissakabusi and I were privileged to spend time with Todd Bennett during his battle with cancer.
“He fought hard, never complained - legend."
Akabusi also paid tribute on Twitter.
“#toddbennett 45.56 sec gun to tape #worldrecord #europeanchampion 1985 you've completed the journey& dipped us on the line #rip & cya soon x"
Bennett ran 45.56 to briefly hold the world indoor 400m record.
Many of the nation’s other sprint stars paid tribute to their friend and mentor.
Athens 4x100m goal medallist Jason Gardener, speaking on behalf of the board of UK Athletics, said: "It is a very sad day for athletics and my thoughts are with Todd's family.
“I, like many, was inspired as a child watching Todd achieve such great success on the track representing Great Britain and Northern Ireland.
"He inspired thousands of young people throughout the UK to take part and enjoy sport as well as raising funds for school sport.
“He will be greatly missed but I am sure his legacy will continue."
Gardener’s team-mate in Greece Darren Campbell worked in business with Bennett.
"Thank you Todd Bennett for allowing me to know a special man, father, husband, athlete and friend. You will always be in my heart! #RIP," he tweeted.
Paula Radcliffe tweeted: "Sad, sad news that Todd Bennett has lost his battle with cancer. RIP.”
- Sports & Recreation
- UK Athletics
- Todd Bennett
- Kriss Akabusi