"Music pioneer"
Many of the tributes point to the fact that Dekker paved the way for groups like Bob Marley and the Wailers.
"The first Jamaican pop act to score a major hit in the UK," said the Jamaica Observer in its obituary.
Host of BBC Radio 2's Reggae Show, Mark Lamarr, described the sudden death as "bizarre".
"I knew him pretty well and am shocked and saddened", said Lamarr.
"Of all the reggae artists, he was the one that did seem like he was going to go on forever - he was extremely fit."
Reggae DJ Daddy Ernie, of Choice FM in London, said: "Any history book that you pick up on reggae, Desmond Dekker's name will have to be in there."
He added: "People like Desmond Dekker only come along once in a lifetime. This is one of the pioneers that has passed away - his place is definitely cemented in reggae history."
Last concert
Desmond Dekker under the Leeds spotlight (Photo: egigs.co.uk)
Desmond Dekker's last concert had been in the northern English city of Leeds on 11 May.
"He was at his peak fitness, he had this big tour coming up for this summer and he was looking forward to it - and then that was it," his manager, Delroy Williams, said.
"He died peacefully but it still hurts. I was his manager and his best friend. I don't think anyone knew how close we were - we go back so far."
He added: "I didn't even get the chance to say goodbye properly."
Desmond Dekker was divorced with a son and daughter.
