Jose Salvador Alvarenga thanked the president of the Marshall Islands, where he was found late last month, before boarding a flight to Hawaii.
He says he left Mexico for a trip in a fibre-glass boat in December 2012 with a friend who died on board.
He apparently survived the 8,000 km (5,000-mile) ordeal by catching fish, birds and turtles with his bare hands.
For fluids, he claimed to have drunk urine, rainwater and the blood of birds.
He was rescued on 30 January by people living on the island of Ebon Atoll.
"Thank you for everything the people of the Marshall Islands have done for me during my stay," Mr Alvarenga, 37, said through an interpreter before leaving for Hawaii. He will make his way from there to El Salvador to be reunited with his relatives.
President Christopher Loeak presented him with a woven garland, the AFP news agency reports.
The fisherman had been due to leave last Friday, but doctors said he needed more rest.
The family of his younger friend say they want to speak to Mr Alvarenga to find out more about how their son died, and what happened to his body.
Known as Ezequiel, he is believed to have starved after being unable to eat raw birds and fish.
Three Mexican fishermen were rescued off the Marshall Islands in August 2006 after what they said was about nine months drifting across the Pacific Ocean.
They survived on rain water, seabirds and fish.
Castaways from Kiribati, to the south, frequently find land in the Marshall Islands after ordeals of weeks or months at sea in small boats.

Bob Pooler, chief instructor with Shropshire Aero Club, said he received a call from the actor, who was keen to rent an aircraft while he was filming the new Star Wars movie.
He said the actor had wanted to bring one of his own planes to Britain, but ran out of time before filming started.
Mr Pooler said the call, from Ford himself, came "out of the blue".
He said he delivered a plane from Sleap Airfield, near Wem, to Denham, close to Pinewood Studios on Sunday.
"I checked Harrison out, flew around the patch with him and made sure he was legal to fly and that's it.
"We talked about Star Wars among other movies."
Mr Pooler, who is also a dealer for Husky light aircraft, said he had first been contacted by the manufacturer's factory a few months ago.
"To rent the aeroplanes from Sleap you have to become a member and Harrison paid his membership dues until the end of the year," Mr Pooler said.
"I asked him, 'can we make you a temporary member of the aero club?' and he said 'I don't want to be a temporary member, I want to be a lifetime member'.
"I proposed that to the committee at the aero club and of course, without hesitation they said let's make him a lifetime member.
"He's got an open invitation to visit us at any time.
"He's also invited me to visit his place in California.
"I think he's got his own mini air force of about 11 aeroplanes."
It is not the first time Ford has been connected with the county.
In 2004 he travelled along the Shropshire Union canal after attending the Llangollen International Eisteddfod in North Wales with wife Calista Flockhart.
A castaway from El Salvador who claims he spent more than a year adrift in the Pacific has begun his journey home.
[NEXT_CONCEPT]
Hollywood actor Harrison Ford has become the latest member of a Shropshire flying club.