The 29-year-old American claimed his 32nd ATP Tour title - his second of the year after his success at Eastbourne in June - with a 1-6 7-6 (7/2) 6-2 victory over the world number 63 from Luxembourg.
Muller started much the stronger of the two players and converted two of his three break points to storm through the first set in 33 minutes.
The left-hander then saved four set points serving at 5-6 in the second to reach a tie-break, but Roddick won five of the first six points and duly took the match into a decider.
And the world number 27 continued where he left off in the tie-break, securing two breaks of serve to go 5-2 up and then serving out the match to love.
The result meant Roddick will head to the London Olympics in fine fettle after his 11th win in 12 matches, while Muller was left still searching for his first ATP Tour crown after his third loss in as many finals.