The 33-1 chance was declared the winner of the famous race courtesy of photo finish, having crossed the line marginally ahead of Sunnyhillboy.
Speaking after the race, Irish jockey Jacob revealed that he thought the win was his destiny.
"You can't beat this," he told BBC Sport. "I was on a tough horse and I said to Paul that one day I would ride you a National winner.
"That was two years ago and now I've done it."
Neptune Collonges was the first grey winner since 1961.