Ben Byrne, 18, set a legal precedent last year when a High Court judge ruled that the three-year time limit on making claims to the Motor Insurers' Bureau - the body which compensates victims of uninsured drivers - did not comply with EU law.
The MIB and Government appealed the decision but last week three appeal judges dismissed their claim, giving Ben the go ahead to secure damages.
They ruled that victims of hit-and-run drivers should have the same rights as those of victims of insured drivers, whose claims can be made until the age of 18.
Ben, of Golborne, Greater Manchester, was just three when he was knocked down outside his nursery school near his home in 1994. The motorist has never been traced.
It was only in October 2001, after taking legal advice, that Ben's parents lodged their application with the MIB. But they refused the claim on the grounds it was out of time.
Lawyers for the MIB and Government argued that the Untraced Drivers Agreement 1972 contains no provision to suspend the three-year time limit until Ben reaches the age of 18.
In a landmark case, Ben's legal team launched an unprecedented damages claim, arguing that there had been a serious failure by the Government to accurately transpose into English law an EU directive which demanded that those injured by hit-and-run or uninsured drivers should be no less favourably treated than other road accident victims.
Mr Justice Flaux, sitting at London's High Court agreed. He said that under EU law the MIB procedure should be subject to a limitation period no less favourable than those governing other minors for personal injury against a traced driver.
The victory is likely to help other victims of hit-and-run motorists who are never caught.
Insurance industry sources denied the appeal court's ruling would lead to thousands of other applications for compensation. They said it would affect only half a dozen claims.
Ben's father, Wayne Byrne, said: "He will be very happy with the result.
"It has been a long time coming, but I think he will be more shocked than anything else because we never expected to win the original case.
"When it first started out we didn't realise just how big a case it was.
"But the further it went the more we realised how significant it could be, not just for Ben but for a lot of other people as well.'
Ben suffered serious leg injuries in the accident. No value has yet been put on Ben's claim.
A spokesman for the MIB said: 'The Department for Transport and MIB strongly defended the claim. MIB will be considering carefully the decision by Judge Flaux and what further steps need to be taken.'