The eight-year-old, who was the smallest horse in the field, held onto the lead, despite Pleasant Company gaining ground in the final metres to force a photo finish.
Tiger Roll’s jockey Davy Russell, 38, was eighth two years ago and third last year, going into today’s race with odds of 10-1.
Russell now takes away the first prize of £500,000.
Afterwards he told ITV: “I’ve won this race a thousand times in my head, in my dreams as a child.
“It’s such a marvellous event, it’s amazing really to have finally done it. I don’t know what to say.”
He also mentioned his mother, who died earlier this year, saying: “She was a marvellous woman, getting up at 6am to drive me around Ireland for races.
“She always did what was best for her children.”
Commenting on Pleasant Company’s last-minute challenge, Russell said: “I did have a big fear – it would have been heartbreaking.”
Trainer Gordon Elliott said: “It’s unbelievable for Davy Russell.
“He’s lost his mother and I’m sure his father Gerry is very proud at home watching. He had a new baby last week, too.
“Coming here I was really worried about the ground. All the way round I couldn’t believe how he was going.”
Tiger Roll is owned by Irish businessman Michael O’Leary, chief-executive of Ryanair.
David Mullins, jockey of Pleasant Company, said: “Davy was going so much better than me.”
Bless The Wings, the winner’s stablemate was third, and Anibale Fly was fourth, with Irish runners dominating the 4.5-mile race.
Bryony Frost, riding in the race for the first time, was the best of the three female jockeys, coming in fifth on Milansbar, trained by Neil King.
Some 26 horses failed to finish the race, either losing riders, pulling up, falling or being brought down.
The horse thought to be in the worst state, Saint Are, was assessed by medics on the track for some time after the race.
Racing Tips later tweeted: “News reaching us is that Saint Are is back in the stables.
“He’s still being treated by the medics, but that has to be a good sign!”
Total Recall was one of the horses to fall, after starting the race as the 7-1 favourite.