During the Yugoslav wars, Nesterović moved to PAOK of the Greek League. While playing there, he obtained a second citizenship to avoid EU restrictions. To obtain Greek citizenship he had to administratively change his name in the eyes of Greek law. While in Greece and other EU countries, he thus competed as a domestic player under the name Radoslav "Rasho" Makris.
Ahead of the 1995–96 season, Nesterović returned to his hometown to play for Union Olimpija. Competing in the Slovenian domestic league, his averages were 30 minutes, 17 points and 14 rebounds per game. The summer of 1996 off season brought another significant feat for Nesterović; while playing for Slovenia's youth national team he was named the MVP at the 1996 FIBA Europe Under-20 Championship. The next season, 1996–97, he was part of that legendary Olimpija team that reached the 1997 EuroLeague Final Four in Rome. In that season, he played an average of 17.0 minutes per game, averaging 8.0 points, and 4.3 rebounds per game in the EuroLeague.
The exposure on the biggest European stage led to a big time move for Nesterović to the Italian League power Virtus Bologna during the summer of 1997. In the first season with his new club, he scored an average of 8 points and grabbed an average of 6 rebounds per game, in the Italian domestic league. In the EuroLeague, he scored 6.5 points and grabbed 6.0 rebounds per game. He helped Virtus win the EuroLeague title, playing alongside legendary players such as Sašha Danilović, Zoran Savić, and Antoine Rigaudeau. In the EuroLeague Final, Nesterović scored 6 points and grabbed 9 rebounds.
NBA
Minnesota Timberwolves
Nesterović was a first-round draft pick of the Minnesota Timberwolves in the 1998 NBA Draft. He joined the Timberwolves just before the end of the 1998–99 season and played there through the 2002–03 season. Nesterović stayed in Minnesota for four full seasons because he played only the last two regular-season games, plus all of his team's games in the playoffs, in his first season. His best season with the Timberwolves was 2002–03, when he averaged 11.2 points and 6.6 rebounds per game, earning himself a 6-year contract with the San Antonio Spurs in 2004. Although the Timberwolves were offering him a contract worth $12 million more, Nesterović opted for the move to Texas for a shot at the NBA title.
San Antonio Spurs
In his first season with San Antonio, Nesterović scored 8.7 points per game and grabbed 7.7 rebounds per game. In his second season with the Spurs, 2004–05, he suffered an ankle injury, and was limited to 70 games. Nevertheless, he remained the starting center for the majority of the season, and, along with his colleague from the Slovenian national basketball team, Beno Udrih, he ultimately won an NBA title with the Spurs that year.
On June 21, 2006, Nesterović was traded to the Toronto Raptors along with cash in exchange for Matt Bonner, Eric Williams and a second round pick in the 2009 NBA Draft. In his first season with the Raptors, he averaged 6.2 points, 4.5 rebounds, and 1.0 blocks per game. On April 2, 2008, at 7:34 pm EST, Nesterović hit his first three-point shot ever in the regular season, with a pump fake, for a buzzer beater against the Atlanta Hawks, in Atlanta. While playing for the Raptors, he was nicknamed Nestea as the fans found it "refreshing to have a true center."
Indiana Pacers
On July 9, 2008, Nesterović was traded along with the Raptors' T.J. Ford, Maceo Baston and the 17th pick in the draft to the Indiana Pacers, in exchange for Jermaine O'Neal and the 41st pick in the draft.
Return to the Toronto Raptors
On July 30, 2009, Nesterović officially was signed by the Raptors, reportedly with the biannual exception of $1.9 million for one season.
For the 2010–11 season Nesterović returned to Europe, when he signed a two-year contract with the Greek League powerhouse Olympiacos. He was released by Olympiacos in July 2011.
National team career
Nesterović was the captain of the senior men's Slovenian national basketball team until his retirement from the national team in 2008. He helped his national team finish in 6th place at the EuroBasket 2005 in Belgrade, and to thus secure a place at the 2006 FIBA World Championship. At the EuroBasket 2005, he played an average of 21.7 minutes, scored an average of 6 points, and grabbed an average of 6.2 rebounds per game.
Nesterović has a sister and five children. He is the godfather to Luka Dončić, the third pick of the 2018 NBA draft. He speaks Serbian, Slovenian, Italian, Greek, and English.
