Roddick bested top seed and two-time defending finalist John Isner 6-4, 6-7 (5-7), 6-4 in one of the semifinal matches, overcoming Isner's 26 aces.
Roddick will be looking to wrap up his second title of the year against the 29-year-old Muller, who will be appearing in his third career final.
The Luxembourg native prevailed over eighth-seeded Go Soeda of Japan in Saturday's other semi, 6-4, 6-3, uncoiling 17 aces and winning 85 percent of his service points.
Roddick is 3-1 lifetime against Muller.
Celebrity Couples of 2014 [PHOTOS]