A native of Belgrade, Serbia and Montenegro, the 6'10" (2.08 m) Stojakovic was selected by the Kings in the first round (14th overall pick) of the 1996 NBA Draft while playing professionally in Greece. He continued to play in Greece until the Kings signed him prior to the 1998-99 season.
After two seasons on the bench in Sacramento, he had a breakthrough season in 2000-01, averaging 20.4 points and 5.8 rebounds per game and shooting .400 from three-point range in his first season as a starter. He finished second in voting for the league's Most Improved Player.
In 2001-02, he played in the NBA All-Star Game for the first time. His scoring average went up to 21.2 ppg, and he reached career highs in shooting percentage (.484) and three-point percentage (.416). His scoring average dropped slightly to 19.2 ppg in 2002-03, but he played again in the All-Star Game. In both seasons, he won the three-point shooting contest conducted during All-Star Weekend.
As a member of the Yugoslavia national team, he earned gold medals at the 2001 European Championships (Eurobasket), held in Turkey, and the 2002 FIBA World Championships, held in Indianapolis. Stojakovic was a member of the all-tournament team in Indianapolis, along with fellow NBA stars Manu Ginobili, Dirk Nowitzki, and Yao Ming.