Axford, who agreed to a minor league deal last month, gets a $2.6 million, one-year contract with a chance to earn more in performance bonuses. The 31-year-old right-hander was 2-4 with a 3.95 ERA in 62 games with Cleveland and Pittsburgh last year.
In six major league seasons, Axford is 24-23 with a 3.40 ERA and 116 saves, including 10 for the Indians last year.
To make room on the 40-man roster, the Rockies placed right-hander Tyler Chatwood on the 60-day disabled list Sunday. Chatwood is recovering from Tommy John surgery last July.
Axford can earn $50,000 each for 35, 40, 45 and 50 games pitched; $100,000 each for 55, 60 and 65 games pitched; and $100,000 each for 30, 35, 40, 45, 50 and 55 games finished.