The Kings announced Stockton's signing Sunday.
The team previously signed him to a 10-day contract earlier this season. He had one point, two rebounds and one assist in seven minutes against the Los Angeles Clippers on Feb. 21 in his only appearance with the Kings.
The 5-foot-11, 165-pound point guard spent most of the season with the Reno Bighorns, the Kings' NBA Development League affiliate. He averaged 20.1 points, 9.4 assists, 4.2 rebounds and 2.5 steals in 43 games for Reno.
The undrafted rookie played in college at Gonzaga, where his father also starred. John Stockton played 19 seasons for the Utah Jazz and retired in 2003 with an NBA-record 15,806 assists.