Towers, who spent the 2010 season as a special assistant to Yankees general manager Brian Cashman, acquired Miranda for right-handed pitcher Scott Allen.
Miranda, 27, hit .253 with four home runs and 14 RBIs over 46 games over the past three seasons with the Yankees. He hit .219 with three home runs for New York in 2010.
Miranda hit .285 with 15 home runs and 43 RBIs for the Yankees' Triple-A affiliate in Scranton/Wilkes-Barre this past season.
One of the areas of need that Towers wanted to address in his first offseason with the D-backs was finding a first baseman to replace Adam LaRoche.
Earlier this month, the D-backs declined to pick up the $7.5 million option on LaRoche's contract for 2011, instead paying him $1.5 million as a buyout.
Allen, 19, was 5-4 with a 3.95 ERA with 95 strikeouts over 28 games over parts of two seasons in the D-backs' Minor League system. He was 4-4 with a 4.73 ERA in 2010 for Class A South Bend.
Allen was selected by the D-backs in the 11th round of the 2009 First-Year Player Draft.