The second-seeded Anderson gained the championship match with a come-from-behind win over Martin Klizan of Slovakia in one of the day's semis, posting a 2-6, 6-4, 6-2 triumph.
Robredo was pounded in the first set but then rallied for a 1-6, 6-3, 6-2 victory over top-seeded Stanislas Wawrinka of Switzerland.
Robredo broke Wawrinka's serve twice in the second set before dominating the third with three breaks, improving to 5-1 lifetime against the Swiss.
Anderson will be seeking his third career title and first clay-court crown, while Robredo will be trying for his 11th overall ATP World Tour title and 10th on clay.
Celebrity Families of 2014 [PHOTOS]