Sedig Benzala, head of the team who operated on him, told the BBC the four-hour operation went well and that the boy remained in intensive care.
He has multiple fractures and concussion.
The Dutch foreign ministry said the boy had told embassy officials his name was Ruben, he was nine-years-old and came from the southern Dutch city of Tilburg. A Dutch couple has flown out to Tripoli to verify his identity.
Ed Kronenberg of the Dutch foreign ministry visited the boy Thursday.
"He's fine, his condition is stable", he told the BBC.
Some of his relatives also arrived Thursday to see him at the el-Khadzra hospital and he smiled and nodded his head.
"It was a very emotional moment," Mr Benzala said.
He added it would take weeks for him to fully recover, but that depended on how his body reacted.
Mr Kronenberg said that the boy was still "very much in shock and also rather dizzy from the anaesthesia he got for the surgery".
"Apparently they found him almost at the front of the crash.
"The first people that came to the rescue noticed he was still breathing and rushed him to a hospital...close to the airport," Mr Kronenberg added.
Dutch Foreign Minister Maxime Verhagen said the boy had muttered "Holland, Holland," to his doctor when asked where he came from.
The head of the European Parliament, Jerzy Buzek, said the boy's survival was "truly a miracle".
The Dutch foreign ministry also said it believed 70 Dutch nationals were killed in the crash. Afriqiyah Airways said at least 59 Dutch citizens died.
Flags across the Netherlands were flying at half mast for the victims on Wednesday.
The Airbus 330 - carrying 93 passengers and 11 crew - crashed on Wednesday as it arrived from Johannesburg, South Africa.
Other passengers included nationals from Libya, South Africa, Germany, Britain and France. The plane's 11 crew, who were also killed in the crash, were all Libyan.
Among the South African victims was award-winning author Bree O'Mara, who also had Irish nationality. She was reportedly on her way to London to sign a book deal.
The Tripoli Medical Center morgue where the bodies have been taken has been cordoned off, and only the relatives of the dead are being allowed in, says the BBC's Rana Jawad in Tripoli.
Libyan TV showed Ruben van Assouw being treated in hospital
Eyewitnesses said the plane started to break up as it came in to land in clear weather.
"It exploded on landing and totally disintegrated," one security official told the AFP news agency.
The plane's tailfin bearing the airline's colourful insignia was the only sizeable piece of wreckage to be seen.
The cause of the crash is not known. The Libyan Transport Minister Mohammed Ali Zidan has ruled out terrorism.
The British Foreign Office confirmed that at least one British national was on board and Irish Foreign Minister Michael Martin later confirmed that an Irish woman was among the dead.
Mr Zidan said victims also included nationals from Germany, Finland, Zimbabwe, the Philippines, South Africa and France, although he had no exact numbers.
According to Airbus, the aircraft was delivered from the production line in September 2009 and had accumulated about 1,600 flight hours in some 420 flights.
Afriqiyah Airways is a Libyan airline founded nine years ago and operates a relatively new fleet of Airbus aircraft, the BBC's Wyre Davies in Cairo reports.
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