The death of the performer, who was last year made an OBE for services to dance and to people with disabilities, was confirmed by the Leeds-based Slung Low theatre company.
Toole died in hospital in the city earlier this week.
Jenny Sealey, artistic co-director of the London 2012 Paralympics opening ceremony, said: "Dave was so many things, our darling, wonderful, opinionated, glorious, silly, funny, kind, sexy, loving and wise friend.
"The most unique and leftfield man ever and funny beyond words.
"And of course, an extraordinary performer and a unique brilliant dancer."
Toole was born with sacral agenesis, meaning his legs did not develop properly, and he had them amputated when he was a young child, according to the BBC.
He began his dancing career back in 1992 after going to a dance workshop in Leeds that integrated disabled and non-disabled dancers.
During the Paralympics opening ceremony he gave a solo performance which saw him hoisted into the air high above the dance floor.
His film credits include the The Tango Lesson and Amazing Grace.
He also performed with the Royal Shakespeare Company.
Alan Lane, artistic director of Slung Low, said: "We are all so sad to hear of Dave Toole's passing.
"It was such a privilege to make so many adventures with him.
"He had an extraordinary talent; he was a brilliant actor and the very finest dancer we've ever seen."
Toole's death was also confirmed by the London-based Candoco dance company, which frequently brings together both disabled and non-disabled performers.
Their artistic director Charlotte Darbyshire said in a statement that Toole was an "exceptional dancer whose outstanding presence and performance changed the dance world".