The 29-year-old has won 11 of his last 12 matches, taking the title in Eastbourne in June, reaching the third round at Wimbledon and now triumphing over Muller in Atlanta.
Roddick made a poor start to the match as he struggled to find his range and rhythm.
Despite Muller winning all but six points when he got his first serve in, the Luxemburger slapped 10 double faults and could only manage to win 15 points behind his second serve.
After the second set went with serve, Roddick stormed through five of the first six points in the breaker before going on to level the match.
The American, who hit 18 aces to Muller’s 20, then had little trouble in the final set as he wrapped up his 32nd Tour title.
Roddick will next fly back to the UK to play alongside John Isner in the men’s doubles for the US team at the Olympics, which begin at Wimbledon next week.