Anderson was claimed off waivers by the Rockies on Friday, Jon Heyman of the New York Post reports.
Anderson was designated for assignment by the Rays on Wednesday but will land with a new organization a few days later. The right-hander tossed five scoreless innings over two relief appearances with Tampa Bay to begin the year. Although he picked up his first career save in early May, he'll likely serve as a middle reliever in Colorado, or he could step in as a starter if Antonio Senzatela (forearm) is forced to miss time.