Smoke started pouring from the 31ft (9.4m) vessel at about 18:30 BST on Saturday, with the man and woman immediately issuing a mayday call.
They were later taken to shore by coastguard volunteers, who hosed down the burning vessel.
Anne-Marie Clark, from Poole Lifeboat, said the couple were in shock.
The fire began while the yacht was in the Swash Channel outside the entrance of Poole Harbour. Hundreds of other vessels were in the area at the time.
Ms Clark said: "A mayday call is used to signal a life-threatening emergency - that they are in grave and imminent danger.
"The next call came through that... they were abandoning ship."
The couple jumped onto a passing motorboat that came to their aid as flames consumed the yacht. They were uninjured.
The area around the burning boat was cordoned off by the lifeboat crew as there were a lot of vessels in the area, Ms Clark said.
Gavin McGuinness, volunteer senior helmsman, said: "The boat on fire required immediate action, as it was a hazard to shipping.
"It could have been an environmental issue if it had gone down, as there were a lot of vessels in the area who were also at risk if the fuel or canisters had gotten alight."
A couple leapt from a burning yacht onto a motorboat after its engine erupted into flames off the coast of Poole.