Dollar - ne Jonny Sharp - died on May 29 at the Royal Marsden hospital at the age of 45. He had been diagnosed with cancer in August 2008.
As well as his work with Massive Attack, Dollar produced Gabrielle's triple-platinum album Rise.
Polydor president Ferdy Unger-Hamilton, who engaged Dollar to work with Gabrielle, called the producer an unsung hero for his work, which included many records that would pave the way for trip hop in the Nineties.
He adds, "I knew Jonny from his work with Neneh Cherry, he co-produced a lot of her work with Cameron McVey and Massive Attack. He also produced Blue Lines. These records had a profound effect on me, Buffalo Stance and Man Child when I was about 14 and when I first heard Unfinished Sympathy like everybody else who heard it, I don't think I could really believe what I was hearing.
"As a fan of these records it was a natural thing for me to call him up when we were looking for a producer for Gabrielle's third album Rise. As committed and driven a producer as I've ever met, I literally had to take the tracks by force back off him, he was so determined to make them perfect. The result was a number one single and album Rise. He was as tough artistically as he was gentle a person."
Dollar is survived by a wife, Harriet, and four children.
He will be buried in a private family funeral in Cornwall, with a London memorial service to follow.