A bank survey suggests that in November new export orders rose at a record rate.
A weaker pound makes UK-produced goods cheaper in overseas markets.
The pound fell sharply against the euro after the Brexit vote and is still well below pre-referendum levels.
The bank's chief economist, Richard Ramsey, said cross-border shopping has also benefited, sending retail sales to their highest level in more than two years.
"Both the manufacturing and retail sectors are expanding at rates well above their pre-downturn historical averages," he added.
Recent official figures also point to export growth - HM Revenue and Customs data for the 12 months to September shows a 6% rise in the value of exports to £7.4bn.
However, Mr Ramsey said the data also points to inflation and consumers should "brace themselves for significant price rises in 2017".
"The downside of a weak currency is import price inflation.
"Manufacturers increased the price of their goods at the fastest rate on record.
"Retailers are also experiencing the highest rate of cost inflation in over eight years."
The Ulster Bank surveys the activity of private sector firms every month, in what is considered a reliable indicator of the economy.

Judge DW Deshpande said the actor would have to be present in the court for the judgement.
Khan has been charged with culpable homicide by the Mumbai court.
He recently told the court he was not driving on the night of the incident.
The actor also said his driver Altaf was driving the car when the crash occurred.
If convicted, he faces 10 years in prison.
Late on the night of 28 September 2002, Khan's Toyota Land Cruiser rammed into the American Express bakery in the Bandra area of Mumbai, authorities say.
The vehicle ran over five people sleeping on the streets, killing 38-year-old Noor Ullah Khan and seriously injuring three others. Another person received minor injuries.
The prosecution has alleged that Khan was driving the car and that he was drunk.
The actor, who has always denied the charges against him, recently told the court that he was not drunk and was not driving the car either.
Khan is one of Bollywood's biggest stars and has starred in more than 80 Hindi-language films.
Several of his films, including Dabangg, Ready, Bodyguard, Ek Tha Tiger, Maine Pyar Kiya and Hum Aap Ke Hain Kaun, have been huge commercial hits.

The 25-year-old full-back moved to New Zealand Warriors for a world-record fee last year after helping Wigan to a league and Challenge Cup double.
"It's somewhere where I'd never say I'd never want to go back to, so at some point in the future it's very possible," Tomkins said.
"I'll never say never. I'll always be a Wigan fan even if I'm not playing there. I love the people, the town."
After announcing his move to the NRL, Tomkins said he could not picture himself playing for another Super League club should he return to England.
After his spell in rugby union, Tomkins' brother Joel returned to Warriors this season from Saracens.
"As soon as Joel signed they were saying 'oh that must mean you're coming back', but for the time being I'm happy playing at the (New Zealand) Warriors," Tomkins told BBC Radio Manchester's Rugby League Extra.
"Watching it as a fan, I'm waiting on results and seeing where it puts Wigan in the league - I've been much more interested in Super League than I have been watching the NRL.
"When you're playing you're concentrating so much on your own game and who you're playing you're not to bothered about other results."
Tomkins scored 13 tries in his 21 appearances in his first season at this new club but they finished outside the play-off places in 11th.
Northern Ireland exporters are continuing to experience a surge in business as a result of the weakening of sterling, the Ulster Bank has said.
[NEXT_CONCEPT]
A court in India will give its verdict on 6 May in a 2002 hit-and-run incident in which Bollywood star Salman Khan is accused of running over five men sleeping on a pavement, killing one of them.
[NEXT_CONCEPT]
Sam Tomkins says he is still open to a return to Wigan Warriors in the future.