Terms of the deal weren't disclosed, but it was reported to be worth $23 million.
Hudson, 38, went 8-7 with a 3.97 earned run average in 21 starts for the Atlanta Braves this past season after missing the second half of the campaign with a fractured right ankle.
After spending his first six seasons with the Oakland Athletics, he was traded to Atlanta in 2004. There he compiled a 113-72 mark with a 3.56 ERA over nine years, including three All-Star Game appearances.
Hudson is 205-111 overall in 15 seasons.