Shaw, 29, spent last season with the Milwaukee Brewers, with whom he struggled to the tune of a .157/.281/.270 slash line and just seven home runs in 86 games. The Brewers demoted Shaw to the minors for portions of the season and non-tendered him following the campaign, after which he was granted free agency.
The slugger was productive during the two previous seasons, however, as he posted a .258/.347/.497 slash line with 63 homers and 15 steals over 157 games played, accruing 3.5 WAR each year.
Toronto has Vladimir Guerrero Jr. and Brandon Drury stationed at third base, with the former possibly spending time at first base and designated hitter next season. Drury has hit .214/.261/.372 with 15 home runs in 128 games with the Blue Jays since being acquired from the New York Yankees.