Member of the public spotted Jesse near Champion St in Williamstown, where he had been staying in a disused building with other people since Tuesday.
He was taken to the Royal Chidren’s Hospital for treatment.
Jesse’s father, Jody, said he and wife Michelle rushed to the police station when told the 15-year-old had been found.
"We got here in about 15 seconds,’’ he said.
Asked if a $50,000 reward for information about their son, posted by Mr Densley's former employer the Lew family and basketballer Andrew Bogut, was still valid, the relieved father said: "Yeah, absolutely.’’
"I would like to especially thank the Lew family, Rose and Solomon Lew. Previous employers of mine I’ve had no contact with for 18 years and without hesitation they put up the first $25,000.
Jesse was last seen by a friend at North Williamstown train station about 8.30am on Tuesday.
He was later captured on CCTV getting off a train at Cheltenham station before boarding a return service to Newport.
Despite several unsuccessful leads, neither police nor Jesse's parents have any idea where he went next.
Jody and Michelle Densley offered a $25,000 reward this morning as the search entered its fourth day.
The figure was then matched by Bogut after the Milwaukee Bucks star heard Mr Densley's pleas on radio.
Today he was taken to Williamstown Police Station where he was united with his relieved family, and waved to reporters before being taken by ambulance to the Royal Children’s Hospital for assessment.
It is understood Jesse was spotted by another boy who called Triple 0.
Ms Densley told Radio 3AW that she was “beside herself” at the discovery.
And despite his visit to hospital, she was confident it was "nothing a good wash and feed won't fix".
The discovery brings to an end an agonising search that included emotional public pleas from his parents.
As late as this morning, Mr Densley and Jesse's mother Michelle said they had no idea where their son was.
Mr Densley said he hoped the money would impel more people to help.
"It's only going to take one person to find Jess," Mr Densley said.
"He's going to be alone I guess. We have have no idea where he is. If we did, we would be looking."
Jesse, who has been suffering depression, has not contacted friends or logged into his Facebook account since his disappearance.
He is described as Caucasian, about 185cm tall and medium build with blond shoulder-length hair.
He was last seen wearing a grey Rip Curl hoodie with a blue panel on the chest.
Police are urging anyone with information to contact Crime Stoppers on 1800 333 000 or to visit www.crimestoppers.com.au – or call 000.