Francis Lagan, understood to be in his 40s, had been head teacher at St Mary’s Primary School in Maghera, Co Derry, for several years and was well known in the local community.
His car was struck by the tree while travelling on the Dublin Road near Antrim, as the storm hit parts of the region with force on Friday.
The road was closed for several hours while emergency services attended. Police later confirmed he had passed away.
At least two people have been killed as Storm Arwen brought gusts of almost 100mph. Cumbria Police said a man from Lancaster died in Ambleside after a tree fell on him just before 11pm on Friday.
Local parish priest Fr Paddy Doherty knew Mr Lagan well from his work at St Mary’s.
Fr Doherty said the news has “stunned the community”.
“He had a great couple of years as principal and had great promise and put in a great amount of work,” he said.
“It is a great loss to the parish and community and we are all stunned by the death. It is a shock — an absolutely terrible evening.
“He was very well known and did a lot of work. He was just a good principal for the school and very much part of the wider community as well.”
Fr Doherty said it was the second tragedy to hit the family in recent weeks.
He added: “I spoke to his wife this evening and his father. His mother only died eight weeks ago so it is an incredibly hard time for the family.
“It will be very hard in the school come Monday. The school and parish staff already have been in touch to put in place support in the school.”
SDLP Mid Ulster MLA Patsy McGlone extended his sympathy to Mr Lagan’s family. “They are well known and respected in the Maghera and wider south Derry area,” he said.
“Our thoughts and prayers are with the entire family at this time. It will affect the wider community, the pupils and the teaching staff and it has a wide ripple effect right around the town of Maghera.
“It’s very sad indeed. It is so sad for everyone concerned.” DUP MLA Pam Cameron described it as an “awful tragedy so close to home”.
The PSNI said: “Police can confirm that a man has died after the car he was driving was struck by a falling tree on the Dublin Road in Antrim on Friday.”
Winds battered large parts of the north-west of the island on Black Friday with shoppers braving the storm.
Thousands of homes were left without electricity, many in the Donegal area, with ESB crews working to restore power.
Ferries were cancelled and some roads were blocked as a result of the gusts and heavy rain.
All of P&O Ferries’ sailings between Larne and Cairnryan were cancelled as a result of stormy seas, with an update from Stenaline expected in the morning.
Ferry sailings between Ballycastle and Rathlin Island were also affected and are expected to remain disrupted.
In England, Friday night’s rugby union Premiership game between Newcastle Falcons and Worcester Warriors was postponed until Saturday evening due to safety concerns.
In North Wales, ITV were forced to pre-record Friday night’s episode of I’m A Celebrity ... Get Me Out Of Here! amid concerns, including that poor weather would meddle with the programme’s broadcast around Gwrych Castle.