The moves were announced after Wednesday's 6-5, 10-inning road loss to the Chicago White Sox.
The switch-hitting Nava was designated for assignment by the Red Sox on July 28.
The 32-year-old batted .152 in 29 games with Boston this season. He also missed 48 games while spending nearly two months on the disabled list with a left thumb sprain.
Nava hit .267 with 23 homers and 169 RBIs over portions of five seasons with the Red Sox.