Storm looked to have missed out on his tour card by the slimmest of margins when he bogeyed the last at the Portugal Masters in October, only to be granted a reprieve when American Patrick Reed freed up a place by declining his exemption.
The Englishman took full advantage in his first tournament of 2017, seeing off McIlroy at the third hole of a play-off to claim his first European Tour title for almost 10 years.
“I can’t quite believe it,” said the 38-year-old.
“This is a dream come true, especially after what happened to me last year. I really took a lot from that experience and told myself to try and grasp the opportunity of getting my livelihood back with both hands and I have done that this week.
"I have been to hell and back. It has been an absolute rollercoaster over the last year and a half. There was pressure today but not the same pressure as trying to keep your European Tour card.”
Storm took a three-shot lead into the final day and finished with a one-under-par round of 71 to leave him on 18 under par.
McIlroy’s 68 forced a play-off, but while Storm parred all the extra holes, the Northern Irishman succumbed at the third.
England’s Jordan L Smith, 24, just missed out on joining the play-off after his 68 left him in third place on 17 under.
“It’s disappointing to finish like that but Graeme has played well all week and what a story it for him,” said McIlroy.
“He thought he had lost his card at the end of last year and there he is now standing with a trophy in his hands after the first event of 2017. I’m delighted for him.”