The ruling is likely to encourage thousands of passengers with similar claims in the UK.
Jet2 argued the compensation payments should be delayed pending the outcome of a similar case in the Netherlands.
But the judge at Liverpool County Court ruled that "a line should now be drawn. Justice delayed is justice denied".
The EU has ruled that airlines must pay compensation for delayed flights, but a number of airlines have yet to pay out.
Four airlines in the UK have made applications to delay payments: Jet2, Thomas Cook, Ryanair and WizzAir.
The Jet2 case heard in Liverpool involved Kim Allen, who claimed â‚¬400 (Â£292) compensation after an almost seven-hour delay when flying from Manchester to Malaga in 2012.
"We've all been kept waiting for so long, but I'm really happy with today's decision," she said after the judge's ruling.
"Hopefully now it's time for the airlines to pay us what the law says they should."
Her solicitor, Kevin Clarke from Bott & Co, said he hoped "the airlines will now finally face up to their obligations to passengers and to settle the hundreds of thousands of legitimate claims outstanding.
"Sadly, the history of their conduct over the last decade would tell us to expect yet another legal challenge."
The issue stems from the 2004 European regulations that oblige airlines, in some cases, to pay compensation to passengers for cancellations and delays, if they are not due to extraordinary circumstances.
A further ruling by the European Court of Justice in 2009 confirmed that delayed passengers should be treated as if their flights had been cancelled, if the delay was longer than three hours, entitling them to cash compensation.
Despite the ruling, a number of airlines in the UK are still arguing that some technical problems should be classified as extraordinary circumstances, and as such, no compensation should be due.
They have also argued that paying compensation for delays of three hours or more is disproportionate and too great a burden.

The Northern Irishman, twice a winner of the European Tour's season-finale, stumbled to a three-over-par 75 to lie joint 55th in a 60-man field.
McIlroy, 27, has never finished worse than 11th in his seven appearances at Jumeirah Golf Estates in Dubai.
Westwood, meanwhile, carded seven birdies and just one bogey in his 66.
The 43-year-old Englishman found out earlier this week he would not be competing in the World Cup in Melbourne next week.
Westwood's partner Danny Willett pulled out because of a back problem, and his place went to Chris Wood.
Under tournament rules, Wood was able to select his own partner and opted for Andy Sullivan.
"I'm disappointed not to be playing," said Westwood.
"I can understand him picking a mate and he has picked a very good player. It is probably more to do with the rules than anything."
The Tour Championship is the final event of the Race to Dubai, with four players still in with a chance of topping the European Tour Order of Merit.
Henrik Stenson, holder of a course-record 25 under at the Earth Course, leads but Willett can leapfrog the Swede should he win the tournament.
Willett would also top the list if he finishes second and neither Stenson nor Alex Noren win in Dubai.
Noren, another Swede, needs to finish at least second and hope Stenson and Willett finish down the field.
McIlroy has an outside chance which requires several permutations falling into place - including Stenson finishing no higher than 46th in the 60-man field.
It took McIlroy 14 holes to register his first birdie of the day, and although he swiftly added another on the next, the four-time major winner double-bogeyed the 16th after needing two attempts - the second minus his right shoe and sock - to play from the edge of a water hazard.
Westwood's former Ryder Cup partner Nicolas Colsaerts and France's Julien Quesne share second place on five under, with Sergio Garcia, Francesco Molinari and Joost Luiten a shot further back.
A county court judge has ruled that airline Jet2.com cannot delay the payment of compensation due to passengers for delayed flights.
[NEXT_CONCEPT]
World number two Rory McIlroy had his worst ever round in the DP World Tour Championship to lie nine shots behind first-round leader Lee Westwood.