At one stage, winds were gusting at 55 knots and winds over 48 knots are not safe for airport staff to work in.
As a result, passengers on nine planes were unable to leave as it was too windy to put access steps in place.
Some passengers were kept on planes for two hours, but wind speeds eventually dropped, allowing them to disembark.
Flights from Edinburgh, Tenerife, Liverpool, Manchester, Birmingham, Newcastle, Glasgow, Gatwick and Bristol landed, but flights, from Luton and Tenerife were diverted to Dublin.
Belfast man Martin Garland was on a flight from Liverpool that landed at 19:30 GMT.
Speaking from the plane, he said: "People are starting to get irritated now and there's a number of elderly passengers that are now getting agitated with the heat on the plane," he said.
"Most people seem to be playing on their phones, the pilot has been getting people up into the cockpit and letting the kids play."
Thomas Spence, who arrived at the airport on a flight from Tenerife, was unable to reclaim his luggage as baggage handlers could not unload baggage from the plane.
Returning to the airport on Wednesday morning to retrieve his bags, he said: "When we were sitting [in the plane], it was rocking on the tarmac.
"You actually thought you were still in the air.
"But it was good to be on the ground because it was a rough flight, it was bouncing everywhere, and we were just glad to get touched down.
"When you came off the plane, it was really windy and you could understand why we were stuck on the plane."
Alan Whiteside, the airport's operations director, said the weather conditions had been "probably the worst we've had in quite a number of years".
"The real issue is the safety of the both personnel operating the steps and the aircraft doors, and the passengers," he said.
"In those kind of winds, those large-sided steps will just start to move, so it's unsafe to put them on unsafe to try to get passengers off.
"It was a fairly horrendous night."

Yanis Varoufakis last week confirmed that he worked on a contingency plan in case emergency funding to the Greek financial system was cut off.
He has been accused of secretly planning a Greek exit from the euro.
But Mr Tsipras said on Friday that he had ordered the plan, adding it would have been "irresponsible" not to do so.
"Of course I issued personal instructions to the finance minister to create a team that would work on a plan of defence in the event of a national emergency,'' Mr Tsipras told parliament, according to AP.
"It would have been politically naive... not to do so. Does that mean... that I was seeking an emergency?" he asked.
Mr Tsipras did not directly address the reported details of the plan, which was to have allowed the government to introduce a parallel payment system if the banking system was closed down and the drachma had to be re-introduced.
A small team in the governing Syriza party was charged with investigating how to secretly copy online tax codes and use them to issue new pin numbers for every taxpayer, to be used in transactions with the state.
"That would have created a parallel banking system while the banks were shut as a result of the ECB's aggressive action to deny us some breathing space," Mr Varoufakis said in a leaked phone conversation.
Mr Varoufakis later confirmed the existence of the plan, but denied claims that he had wanted to engineer a Greek exit from the euro.
Earlier this month eurozone leaders agreed to offer Greece a third bailout of â‚¬86bn, after marathon talks in Brussels.
However the details of the bailout remain to be negotiated between Greece and its creditors.
Passengers flying into Belfast International Airport were prevented from getting off planes for a time on Tuesday night due to high winds.
[NEXT_CONCEPT]
Greek Prime Minister Alexis Tsipras has defended his former finance minister in a row over an "emergency plan" drawn up in case of Greece's exit from the euro.