The Yomiuri Giants did not provide any financial details.
The 34-year-old Smoak broke in with the Texas Rangers in 2010 and has also played for Seattle and Toronto. He is a switch-hitting batter and has a career average of .229 with 196 home runs. He was an All-Star in 2017.
He hit only .176 in the short season last year with the Brewers and Giants.
The Yomiuri Giants won the Central League last season but lost in the Japan Series to the Fukuoka Softbank Hawks in four games.