Wagner started his basketball career in the youth ranks of Alba Berlin. In 2013–14, Wagner played for the club's under-19 Bundesliga squad, which won the German championship. In 2014–15, he played on Alba Berlin's Bundesliga roster.
College career
Wagner first came to the attention of University of Michigan head coach John Beilein in 2014 through an email from a former coaching acquaintance in Germany. Wagner also used social contacts to forward a self-made highlight video to Beilein. Ultimately, Beilein flew to Berlin to recruit Wagner. In April 2015, Wagner announced his decision to attend the University of Michigan and play for the Michigan Wolverines. By opting to go to college, he turned down an offer to play professionally.
Wagner's five steals in the March 9, 2017 Big Ten Conference Men's Basketball Tournament opener against Illinois was a single-game high for the tournament. Three days later, Michigan won its first Big Ten Tournament championship since 1998. On March 19, Wagner's career-high 26 points helped Michigan defeat Louisville 73–69 to advance to the Sweet 16 of the 2017 NCAA Division I Men's Basketball Tournament. For the season, Wagner started all 38 games and averaged 12.1 points and 4.2 rebounds per game, while shooting 39.5% on three-pointers. He finished the season as the team's leading rebounder. Following the season, he was an honorable mention All-Big Ten selection by both the coaches and the media. On April 10, 2017, both Wagner and teammate D. J. Wilson declared for the 2017 NBA draft, but did not hire agents, which gave them until May 24 to withdraw their names and retain their athletic eligibility to return to Michigan. Declaring early enabled him to participate in workouts with NBA teams and made him eligible for an invitation to the May 9–14 NBA Draft Combine. On April 30, 2017, Jeff Goodman of ESPN reported that he was invited to the NBA Draft Combine. On May 24, 2017, Wagner decided to pull out of the 2017 draft and return to Michigan for the 2017-18 season.
Junior season
Wagner was selected to the 2017 10-man preseason All-Big Ten team. He was also one of two Big Ten players named to the 21-man Karl Malone Award watch list. He was a preseason John R. Wooden Award and Naismith College Player of the Year watchlist honoree. On January 13, 2018, Wagner scored a career-high 27 points as Michigan defeated the fourth-ranked Michigan State Spartans 82–72 in East Lansing; Wagner shot 8-for-13 from the field, including 3-for-4 from three-point range and 8-for-8 from the free-throw line. Following the 2017–18 Big Ten Conference men's basketball regular season, Wagner had accumulated more three-point field goals than any NCAA player or taller and was a second team All-Big Ten selection by the coaches and the media. On March 2, Michigan defeated Nebraska 77–58 in the quarterfinals of the 2018 Big Ten Conference Men's Basketball Tournament. Wagner recorded his seventh double-double of the season with 20 points and 13 rebounds. His 13 rebounds marked a single-game high for the 2018 tournament through the first two rounds. The following day, in the semifinals of the Big Ten Tournament Wagner scored his 1,000th career point, becoming the 54th Wolverine to reach the milestone. He finished the game with a team-high 15 points and eight rebounds in a 75–64 victory over the second-ranked Michigan State Spartans. In the March 4, 2018 Big Ten Tournament championship game against Purdue, Wagner scored 17 points to help lead Michigan to their second consecutive Big Ten Tournament championship. Wagner was named the tournament's Most Valuable Player. In the 2018 tournament, Wagner averaged 15.8 points and 6.5 rebounds per game. Wagner, who averaged 12.5 points and 5.5 rebounds in the first four games of the 2018 NCAA Basketball Tournament, was joined by Wolverines teammates Matthews and Muhammad-Ali Abdur-Rahkman on the West Region All-tournament team. Having reached the Final Four, Michigan defeated Loyola–Chicago 69-57 in the national semifinals on March 31. Wagner recorded his eighth double-double of the season with a game-high 24 points and a career-high 15 rebounds. Wagner became the first player with at least 20 points and 15 rebounds in a national semifinal game since Hakeem Olajuwon in 1983. On April 2, Michigan lost to Villanova 62-79 in the National Championship Game. Wagner recorded 16 points and seven rebounds, and was named to the Final Four All-Tournament Team. For the tournament he averaged 15.0 points, 7.3 rebounds, 1.3 assists, and 1.2 steals, while shooting 38.5% on his three-point shots. For the season, Wagner averaged 14.6 points and 7.1 rebounds and shot 52.8% overall and a team-best 39.4% on his three-point shots. On March 21, Wagner became an Academic All-Big Ten honoree. On April 14, 2018, Wagner announced that he would enter the 2018 NBA draft and hire an agent. On May 1, Wagner signed with Roc Nation's Joe Branch, who has represented former Michigan teammate Caris LeVert. Later that day, he received an invitation to the NBA Draft combine.
Professional career
Los Angeles Lakers (2018–2019)
On June 21, 2018, Wagner was selected with the 25th overall pick in the 2018 NBA draft by the Los Angeles Lakers. On July 1, he signed his rookie scale contract with the Lakers. On July 10, Wagner injured both his left knee and left ankle in the Las Vegas Summer League. He was sidelined for all of training camp and the preseason by the knee injury. Wagner was assigned to the South Bay Lakers on rehab assignment on October 26. Wagner made his G-League debut for the South Bay Lakers on November 3, scoring 17 points in 29 minutes in a 108–106 loss to the Stockton Kings. He made his NBA debut on November 17 against the Orlando Magic. On December 2, in a 120–96 victory against the Phoenix Suns, Wagner scored his first NBA points and finished the game with 10 points. On March 9, 2019, Wagner scored a career-high 22 points with six rebounds, three assists and a block in his first career start in a 107–120 loss to the Boston Celtics.
Washington Wizards (2019–present)
On July 6, 2019, Wagner was traded to the Washington Wizards, along with Isaac Bonga, Jemerrio Jones, and a 2022 second-round pick, in a three-team trade. This was necessary for the Lakers to clear cap space to acquire Anthony Davis. On November 15, playing against the Minnesota Timberwolves, Wagner became the first NBA player to score 30 points and obtain 15 rebounds coming off the bench since Yao Ming in 2002 and the first to post such numbers in under 26 minutes played in since Len Chappell in 1967. Wagner also drew three charges in the game and was the first NBA player to ever post 30 points and 15 rebounds with 4 three-point shots off the bench. Wagner missed 24 games with an ankle sprain before returning to the lineup on February 3 against the Golden State Warriors. He was named to the Rising Stars Game at the 2020 NBA All-Star Weekend, where he scored 16 points for the world team.