He goes on the club's 40-man roster, putting them at a full 40 for now.
Beliveau, 25, made his big-league debut in 2012 in the Cubs' bullpen, going 1-0 with a 4.58 ERA in 17 2/3 innings.
He spent most of the season at Triple-A Iowa and was 4-5 with a 3.89 ERA in 44 innings (37 appearances).
He was designated for assignment on Dec. 12 when the Cubs signed third baseman Ian Stewart.
Beliveau, the 2011 Cubs minor league pitcher of the year, was taken by Chicago in the 18th round of the 2008 draft. He has averaged 11.6 strikeouts per nine innings in his five-year minor league career.