The 29-year-old appeared in 23 games for the Rockies last season and posted a 3-2 record with a 6.12 ERA. In parts of four Major League seasons, Moscoso has an 11-12 record with a 4.16 ERA in 57 games, including 24 starts.
The Blue Jays now have one vacant spot on their 40-man roster.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. Adam Berry is a reporter for MLB.com. Follow him on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.