The team also agreed to a one-year deal with outfielder Brandon Barnes that avoided arbitration.
Axford had 25 saves for the Rockies last season. He also dealt with personal issues away from the field as his young son recovered from rattlesnake bites suffered during spring training in Arizona.
Rosario was signed by Colorado as a non-drafted international free agent in 2006. He hit .268 with six homers in 87 games last season while the team tried to convert him from catcher to first base.