Roddick came through 6-4 4-6 7-6 (9/7) 7-6 (7/5) to see off the Scot.
Murray had beaten Roddick in six of their eight previous meetings.
For Roddick, a third Wimbledon final is the biggest achievement so far of a year in which he has appeared rejuvenated.
The American began working with renowned coach Larry Stefanki in December and, after an off-season spent focusing on his fitness, Roddick has reaped the benefits.
Tomorrow’s match against Federer, a rematch of the 2004 and 2005 finals that the Swiss won, will be Roddick’s first appearance in a grand slam showpiece since the US Open final in 2006.
Reflecting on his win over Murray, the 26-year-old said: “In recent years, it’s certainly up there (with my best matches).
“Playing a player of his rank, his calibre, in his atmosphere. He was certainly in form going into the match. I had to play my best tennis to win.
“You don’t go back to a Wimbledon final by accident. It certainly is a process. And it’s probably been a longer process than I would have liked. But I’ve enjoyed everything that has gone into it.
“I did work real hard and have been committed from everything to diet to sleep to everything. So I certainly gave myself every opportunity to succeed.
“I didn’t know if I was going to get to play a final of Wimbledon again, I’m certainly thankful to have that opportunity.”
Roddick pinpointed the first game of the third set, where he recovered from 0-40 to hold serve, as the decisive moment. “You’re probably not going to get out of a 0-40 hole too often against a guy who returns like him,” he continued. “So that was definitely key, to get through that.”
After his triumph, Roddick knelt down on the stairs leading away from Centre Court in a moment of contemplation.
“I didn’t know anybody saw that,” he admitted. “It was just me taking a second to try to make myself maybe believe that I was actually going to the locker room having done that.”
Murray put a brave face on the defeat — making this summer’s US Open his next target for glory.
The 22-year-old said: “The way that I played this year it was very, very close to getting to the final.
“I believe I can win a grand slam, whether it’s Wimbledon or US Open or Australia or whatever, I’m going to give myself chances. I’ll come back next year and try to do better.”
Roddick faces a huge task if he is to beat Federer, however.
Federer will call on all his vast experience of Wimbledon finals to stay composed as he attempts to break Pete Sampras’ record of grand slam victories.
The Swiss ace produced another masterclass to ease past Tommy Haas in straight sets in the first men’s semi-final on Centre Court and reach a record magnificent seventh successive final.
Federer, who broke Bjorn Borg’s record of five consecutive Wimbledon victories two years ago, drew level with Sampras with his 14th slam at Roland Garros last month and is not expecting any big-match nerves tomorrow.
“I don’t think so because it helped me a lot trying to achieve the fifth straight Wimbledon, equalling Borg’s record,” he said.
“For some reason that meant the world to me. I was in a bubble for two weeks just trying to achieve it.
“So this time around I think I’m much more relaxed. Maybe it’s also because of Paris but I really thinkthat experience, trying to go for my fifth Wimbledon, was a really big one.”
Federer is still waiting to see if Sampras will come to Wimbledon for the final, but Borg was in the Royal Box to witness the world number two edge to within one win of his own Wimbledon total of 51.
It was all too easy as Federer maintained his 100% record in Wimbledon semi-finals with a 7-6 (7/3) 7-5 6-3 victory.
A fifth straight-sets win of the Championships was just about his most comfortable as he denied Haas a single break point.
Error-free on serve, Federer caused no end of frustration for his opponent with his ability to land the ball on a sixpence.