Ryan Baird, 39, who was from Larne, had been living in Dumfries and Galloway.
Eighteen other people were taken to hospital and three are still being treated for non-life threatening injuries.
The coach was carrying supporters to Ibrox Stadium.
Mr Baird still had close ties with Larne Rangers supporters club where friends have been leaving tributes to him.
He was described by his cousin Louise Evanne Baird as "amazing".
Mr Baird's partner Sarah Hughes, paid tribute to him, saying he had loved the club.
The Nith Valley Loyal Rangers Supporters Club posted on its Facebook page: "The club would like to thank everyone for their good wishes & concern at this sad time."
RangersLinfieldFC tweeted: "We have been informed that the man who sadly passed away was a Rangers and Linfield fan named Ryan Baird from Larne, Northern Ireland, RIP."
In a club statement, Rangers said it was "deeply saddened" by the crash, adding: "Our profound condolences go to the gentleman who has died and our thoughts are with his family.
"We are also thinking of those who have been injured and taken to hospital."
Rangers managing director Stewart Robertson said: "Everyone at the football club and every member of our Rangers family is thinking of all of those caught up in this terrible accident.
"Clearly this is a deeply distressing time and the board extend our deepest sympathies and concerns."
Celtic also passed on their condolences in a club statement, saying: "In relation to news of today's accident involving Rangers supporters on their way to the match, everyone at Celtic sends our sincere condolences following the death of a supporter."
The crash happened at about 13:15 BST on Saturday on the A76 by the Crossroads Roundabout near Kilmarnock.
The coach was taking the Nith Valley Loyal Rangers Supporters' Club to Ibrox Stadium, where Rangers were due to play Partick Thistle in the Scottish Premiership.
One passenger said the bus, which had 37 people on board including the driver, had "swerved" before landing on its side on a grass verge.
The family of a man originally from County Antrim, who died after a coach carrying Rangers fans overturned on the outskirts of Kilmarnock, have travelled to Scotland.