The 16/1 son of Frankel, who was only ridden by jockey Adam Kirby after he lost the ride on John Leeper to Frankie Dettori, powered clear in the final furlong to give his Appleby another Derby winner after Masar in 2018.
Richard Hannon's Mojo Star, a 50-1 chance, ran a huge race to be four and a half lengths away in second, with the winner's stablemate Hurricane Lane another three and a quarter lengths back in third.
Oisin Murphy was booked for Adayar, but Kirby then replaced him on Thursday.
Kirby told ITV Racing: "There's been ups and downs, it's racing, but when it comes to Charlie Appleby, he's a top man. I can't thank him enough. He's a real gentleman and a great trainer."
Appleby said: "All the credit goes to Sheikh Mohammed and Team Godolphin. We spoke on Wednesday night after the horses did their breeze in the morning and I'll be honest, I said to His Highness I couldn't be happier with them all, but I did feel this horse was more a Leger horse, and he said 'Charlie, run him, there's only one Derby.
"As always, he's right.
"But from the team's point of view, it's fantastic, they all work so hard.
"I'm delighted for Adam, it was a fantastic ride and it's something all jockeys want to achieve."
Gear Up set the early gallop, with Kirby on his heels aboard Adayar and Youth Spirit also prominent in the early stages.
Favourite Bolshoi Ballet was also towards the head of the field, settled in fourth on the outside, while the well-fancied John Leeper was restrained in last place by Dettori until the field reached Tattenham Corner.
Gear Up started to drop away with two furlongs to run, allowing Kirby a run up the inside rail and he soon put daylight between himself and the field.
Mojo Star finished well from off the pace, with Hurricane Lane also keeping on at the one pace for minor honours, but Aidan O'Brien's Bolshoi Ballet and the Ed Dunlop-trained John Leeper were both ultimately well-beaten.
Bolshoi Ballet was sent off the 11/8 market leader, but could finish only seventh as the only representative from Ballydoyle this year.
O'Brien said: "He just ran a bit lifeless. What the reason was, I'm not sure.
"It doesn't work every day. That's the way life is.
"I don't want to make excuses because I don't want to take away from the other horses.
"He was in the perfect position. He wants nice ground and maybe that was the reason."