The 34-year-old Montero finished last season with the Toronto Blue Jays. In June, he was designated for assignment by the Chicago Cubs a day after he blamed teammate Jake Arrieta for allowing seven stolen bases in a loss against Washington.
Montero said the Nationals ran on the 2015 NL Cy Young Award winner because they knew he was slow to the plate with his delivery.
He said at the time: "So it's just like, `Yeah, OK, Miggy can't throw nobody out,' but my pitcher doesn't hold anybody on."
The highlight of Montero's Cubs' tenure was a big hit late in Game 7 of the 2016 World Series that helped end the team's championship drought. But he threw out only one of 31 potential base-stealers while with Chicago last season.
Montero has a career .257 average with 126 homers and 550 RBIs since making his debut in the majors in 2006.