“I started to wonder if it would ever be my time,” said McIlroy, who shot a one-over 73 on the final day to tie with Rose on 11 under.
“The past 10 years [I’ve been] coming with the burden of the Grand Slam on my shoulders and trying to achieve that.
“I am so proud to be able to call myself a Masters champion.
“It’s been very difficult. And not just about winning my next major, but the career Grand Slam.”
McIlroy’s travails have been an annual talking point coming into the iconic tournament which takes place every April and is the first of the year’s majors.
“What are we all going to talk about next year?” McIlroy, with a beaming smile on his face, asked the media after his victory.
“It’s a dream come true. I have dreamt about that moment for as long as I can remember.
“Watching Tiger Woods in 1997, and then winning his first Green Jacket, I think that inspired so many of my generation to want to emulate what he did.”
English veteran Rose, who was also aiming for his Masters victory, courageously fought back to force the play-off with a final-round 66.
He had some nice words for his long-time friend McIlroy, before revealing what he told the new Masters champion on the 18th green.
“I just said, listen, this is a historic moment in golf, isn’t it, someone who achieves the career Grand Slam,” said Rose.
“I said it was pretty cool to be able to share that moment with him.
“Obviously I wanted to be the bad guy, but still, it’s a momentous occasion for the game of golf.”
McIlroy’s Ryder Cup team-mate Shane Lowry, who faded out of contention on Sunday with an 81, told BBC NI Sport: “It’s huge for Irish golf. It’s huge for everyone. I’ve had a really bad day but I’m delighted for him.
“He might not have wanted to say this but it’s genuinely been everything for him over the past 10 years.”
Lowry also commented on X, where Ireland’s 2019 Open champion wrote: “He always said to me he’d retire a happy man if he won the Green Jacket.”
England’s Tommy Fleetwood said it was “a very Rory McIlroy way of doing it” and nobody could “have written a better script”, adding: “I couldn’t be happier for him. He’s at the top of his game and he’s achieved something incredible.”