The five-year veteran hit .157 with seven home runs in 86 games last season for the Milwaukee Brewers. Shaw, 29, hit a career-high 32 home runs for the Brewers in 2018, while posting a .241 average in 152 appearances. Shaw owns a career .243 average with 99 home runs. He played his first two seasons for the Boston Red Sox before being traded to the Brewers in 2016.
Shaw is expected to play mainly at first base for the Blue Jays, while also appearing at third base and as a designated hitter, when needed.