Bjelica began his professional career in the 2007–08 season with the Arkadia Traiskirchen Lions of the Austrian League.
After one season abroad, he returned to the Serbian team Crvena zvezda, and spent two successful seasons there, under head coach Svetislav Pešić. During the 2008–09 season, he made breakthroughs, and earned a place in the first lineup. He was particularly noted for his performance during the EuroCup, for his outside shooting. Later in his career, Bjelica cited coach Pešić as one of the main reasons for his improvement as a player. Coach Pešić trusted Bjelica with the ball, and gave the 6"10 Bjelica a primary ball handler role on several occasions, which helped to develop Bjelica as a play-maker.
Bjelica was drafted by the Washington Wizards with the 35th pick of the 2010 NBA draft. His draft rights were then traded to the Minnesota Timberwolves.
In August 2010, Bjelica signed a five-year contract with Spanish club Saski Baskonia. In his first season with the club, he didn't get much playing time, averaging only 9 minutes played per game. In his second season with Baskonia, he averaged 4.8 points per game, on 56% shooting from the field, and 47% shooting from 3 point range, three in 13 minutes played per game. His third and last season with the club was the most successful, as he played in 26 games, with the averages of 9.9 points, 4.8 rebounds, 1.3 assists, and 1 steal per game, on 46% shooting from the field.
On July 22, 2013, Bjelica signed a three-year deal with the Turkish team Fenerbahçe Ülker, which was led by one of Europe's great coaches, Željko Obradović. He cited Obradović as the main reason why he didn't go to the NBA instead. In the 2013–14 season, he already became one of the key Fenerbahçe Ülker players, averaging all career-highs of 10.4 points, 6.1 rebounds, 2.2 assists, and 1.6 steals per game, over 24 EuroLeague games.
The following season, Bjelica's game saw its most improvement and consistency. On March 30, 2015, he was named the EuroLeague MVP of the Month for March, his first such monthly award in his career. Over 4 games played in March, he averaged 15 points, 9 rebounds, 3 assists, and 1 block per game. In May 2015, he was chosen to the All-EuroLeague First Team, for his performances over the season. Eventually, Bjelica was named the EuroLeague MVP of the season. Fenerbahçe also advanced to the EuroLeague Final Four for the first time in the team's history. On May 15, 2015, however, they lost in the semifinal game to Real Madrid, by a score of 87–96. Eventually, Fenerbahçe finished in 4th place, after losing in the third-place game to CSKA Moscow, by a score of 80–86. Bjelica had his best season since coming to the club, averaging a career-high 12.1 points, 8.5 rebounds, 1.9 assists, and 1.3 steals per game. Fenerbahçe, however, finished the season without winning any trophy, after also losing in the semi-final series of the Tukish League championship, to the eventual league champions Pınar Karşıyaka.
On July 1, 2015, Bjelica opted out of his contract with Fenerbahçe in order to play in the NBA.
On July 14, 2015, Bjelica signed with the Minnesota Timberwolves. He made his debut for the Timberwolves in their season opener on October 28, 2015, recording eight points and five rebounds in a 112–111 win over the Los Angeles Lakers. On November 7, 2015, he had a season-best game with 17 points, 11 rebounds, five assists, one steal and one block against the Chicago Bulls. On April 7, 2016, he scored a season-high 18 points against the Sacramento Kings. Four days later, he recorded 11 points and a season-high 14 rebounds against the Houston Rockets.
On November 13, 2016, Bjelica made his first career start and scored a career-high 24 points in a 125–99 win over the Los Angeles Lakers. On March 16, 2017, he was ruled out for the rest of the 2016–17 season with a left foot injury. He underwent surgery five days later to repair a fractured navicular bone in his left foot.
Bjelica played with the senior Serbian national basketball team that won the silver medal at the EuroBasket 2009. He was also a member of the Serbian national team at the 2010 FIBA World Championship, where Serbia was defeated 99-88 by Lithuania in the game for the bronze medal, after they had earlier lost to hosts, Turkey, in a highly controversial semifinals finish. He was also capped for the national team of Serbia at the EuroBasket 2011, in Lithuania, where Serbia finished eighth.
During EuroBasket 2013 in Slovenia, Bjelica became one of the veterans of a very young and incomplete Serbia squad, leading the team alongside captain Nenad Krstić and Nemanja Nedović. Serbia was eventually swept by Spain in the quarterfinals, but the team showed some good performances, particularly against Lithuania and France. During the tournament, he averaged 10 points, 7 rebounds, and 1.9 assists per game, on 54% shooting from the field.
He was also a member of the Serbian national basketball team that won the silver medal at the 2014 FIBA Basketball World Cup under head coach Aleksandar Đorđević. Although his three point shooting form wasn't impressive during the tournament, he was still one of the most important players of the team, filling all sorts of roles with his handling, passing, rebounding, and scoring. He ended the tournament with averages of 11.9 points, 6.9 rebounds, and 2.8 assists per game.
He was also a member of the team that represented Serbia at the EuroBasket 2015. In Serbia's opening game, an 80–70 win against Spain, he was Serbia's key player, posting 24 points, 10 rebounds, and 4 assists. The following day, he made a game-winning shot against Germany. In the last match of the group phase, he scored 19 points, grabbed 8 rebounds, and had 4 assists against Italy. Serbia dominated in the tournament's toughest group, Group B, with a 5-0 record, and then eliminated Finland and the Czech Republic in the round of 16 and quarterfinal games, respectively. However, they were stopped in the semifinal game by Lithuania, by a score of 67–64, and eventually lost to the host team, France, in the bronze-medal game, by a score of 81–68. Being one of the team's leaders, along with Miloš Teodosić and Miroslav Raduljica, Bjelica averaged 13.9 points, 6.6 rebounds, and 2.7 assists per game, on 56.1% shooting from the field and 37.5% shooting from behind the three-point line.
Bjelica was brought up in the New Belgrade Blocks. He is married to Mirjana. Their wedding took place in June 2012.Club
2014–15 EuroLeague Final Four with Fenerbahçe
Turkish Basketball League: 2013–14
Turkish President's Cup: 2013
2009 Best Sportsman of SD Crvena Zvezda
2015 March Euroleague MVP of the Month with Fenerbahçe
2015 All-EuroLeague First Team
2015 EuroLeague MVP
Note: The EuroLeague is not the only competition in which the player participated for the team during the season. He also played in domestic competition, and regional competition if applicable.