The 26-year-old ended Britain’s 77-year wait for a men’s singles winner with a 6-4 7-5 6-4 triumph.
Murray played the better tennis during the match but had to fight back from 4-1 down in the second set and 4-2 behind in the third to triumph in three hours and nine minutes.
The final game was a fitting conclusion to a historic occasion, with Murray seeing three match points disappear and then having to save three break points before finally clinching it when Djokovic netted.
Murray raised his fists in celebration before embracing Djokovic then sinking to his knees with his forehead on the grass.
Murray’s emotions were a total contrast to last year, when he had sobbed through his post-match speech after losing the final to Roger Federer.
“It feels slightly different to last year,” Murray said. “Last year was one of the toughest moments of my career, so to manage to win the tournament today...
“It was an unbelievably tough match, so many long games.”
That match against Federer proved a turning point, with the Scot going on to win Olympic gold by beating Federer on the same court four weeks later and then winning his first grand slam title at the US Open.
Murray had said after his semi-final win over Jerzy Janowicz that it would be tough to top those moments, but this was very special.
Murray said: “I also said that winning Wimbledon is the pinnacle of tennis. The last game almost increased that feeling. I worked so hard in that last game.
“Mentally, that last game will be the toughest game I’ll play in my career, ever.
“It was a different match to the US Open. Winning Wimbledon, I still can’t believe it. I can’t get my head around that.
“It was just an amazing finish to the match. I was glad I managed to see all of my team afterwards. They saw what it was like last year after the match. It was a completely different feeling this year.
“This one will take a little while to sink in, I’m sure.”
Murray made special mention of (Coach Ivan) Lendl, who tried so hard to win Wimbledon during his own career but was twice a beaten finalist.
“This one is especially for Ivan as well,” Murray said, “because I know he did everything to try to win this when he was playing, and I’m glad I was able to help him out when he was coaching.”
The pair spoke afterwards, and Murray said: “He just said that he was proud of me, which obviously coming from him means a lot.
“He doesn’t smile in public too much, but when he’s away from the crowds and the cameras he’s a very different character.
“I think he believed in me when a lot of people didn’t. He stuck by me through some tough losses the last couple of years. He’s been very patient with me. I’m just happy I managed to do it for him.
Asked by on-court interviewer Sue Barker about the “torturous” nature of the final game, Murray said: “Imagine playing it.”
“I’ve played Novak many times and when everyone’s finished playing he’s going to down as one of the biggest fighters.
“He’s come back so many times from losing positions and he almost did the same again today.
“That made it extra tough and I just managed to squeeze through in the end.
“That win was for myself but I also understand how much everyone else wanted to see a British winner at Wimbledon. ”
World number one Djokovic was graceful in defeat, saying: ““Congratulations to Andy, you absolutely deserved this win, you played incredible tennis.
“Congratulations to his team. I know how much it means to them. I know how much it means to you guys in this country. Well done.”
The crowd roared their approval of the Serbian in acknowledgement, before Djokovic was reminded of how intense the pressure has been on Murray at Wimbledon.
“That makes his success even bigger. I’m aware of the pressure he gets,” Djokovic said. “Definitely there’s a lot of expectations of him.
“I gave it my all, it was a pleasure to be part of this match, this final. Thank you.”