It was a third winner of the big race for Irish trainer Aidan and a first for his 19-year-old son.
Main Sequence (9-1), the mount of Ted Durcan, made late ground to take second place in the nine-strong field with O'Brien's second string Astrology (13-2), finishing third after making much of the running under jockey Ryan Moore.
O'Brien junior said: "He did well to win today. He's a very special horse and I'm very fortunate to be on his back."
His proud father said: "We were afraid even to dream. No words I can say can describe this and there was no dream big enough."
Camelot raced towards the rear early on while stable mate Astrology cut out the pace and turning into the straight still had plenty to do.
OBrien jnr. then reeled in the front-runner with 200 metres left and the colt raced away like a truly top-class performer.
The winning jockey, aware of the unique character of the Epsom track, said: "This was his first time coming down a hill and round those bends so he was green and backing off a bit. He quickened up well and will have learnt a lot from today."
O'Brien senior won the Epsom Oaks on Friday with 20-1 shot Was and also captured the first two classics of the season, the 2,000 Guineas, with Camelot, and the 1,000 Guineas.
Camelot is now in line to emulate Nijinsky in 1970 by winning the Triple Crown of the 2,000 Guineas, Derby and St Leger, the final classic at Doncaster in September.
Bookmakers make the colt a near certainty to achieve the feat, quoting odds of 1-3. Victory in the St Leger would also mean an unprecedented sweep for his trainer in one year of all five English classics.
Part owner Derrick Smith, a key member of the Coolmore operation, said: "The Triple Crown must be on the agenda mustn't it? We may get pressurised into it but we'll sit down with Aidan and make the final decision."
The St Leger is run over 2.9 km, compared with 1.6 km of the Guineas and 2.4 km of the Derby and a horse needs to be special to combine speed with stamina at the top level.
David Lanigan, having his first Derby runner with the previously unbeaten Main Sequence, said: "He did everything right in the race and was second to a very good horse."
The race, run in bright sunshine, was watched as usual by Britain's Queen Elizabeth on the opening day of four days of festivities to mark her Diamond Jubilee.