Harris attended Hamilton Southeastern High School in Fishers, Indiana. As a sophomore in 2009–10, he averaged 14 points, four rebounds, two assists and three steals per game as he led Hamilton SE to a 17–4 record. As a junior in 2010–11, he averaged 18.6 points, 5.0 rebounds, 3.0 assists and 2.7 steals per game as he led the Royals to a 20–4 record and a trip to the Class 4A regional finals, capturing just the second sectional championship in school history.
In November 2011, Harris signed a National Letter of Intent to play college basketball for Michigan State University.
As a senior in 2011–12, Harris averaged 25.4 points, 7.4 rebounds, 3.1 assists and 4.0 steals per game as he led the Royals to a 22–3 record, advancing to the Class 4A sectional final. He finished his high school career with a school-record 1540 points (16.7 ppg), 467 rebounds (5.1 rpg), 232 assists (2.5 apg) and 232 steals (2.5 spg).
Harris was rated among the top players in the nation by ESPNU100 (No. 11), Scout.com (No. 16) and Rivals.com (No. 25). He was also ranked among the nation's top shooting guards by ESPNU100 (No. 2), Scout.com (No. 4) and Rivals.com (No. 7).
Harris was also an outstanding football player at Hamilton SE, playing wide receiver in his sophomore, junior and senior years. He won three league championships, while also adding a sectional championship as a senior.
As a freshman at Michigan State in 2012–13, Harris was named the Big Ten Freshman of the Year, becoming the first Spartan to win the award since 1986. He was also a second-team All-Big Ten selection and a Big Ten All-Freshman Team honoree. In 34 games (33 starts), he averaged 12.9 points, 2.5 rebounds, 1.4 assists and 1.2 steals in 29.7 minutes per game.
As a sophomore in 2013–14, Harris earned first-team All-Big Ten, All-Big Ten Defensive Team, USBWA All-District selection, first-team NABC All-District, and an honorable mention Associated Press All-American honors. In the season opener against McNeese State, he recorded his first career double-double with 20 points and 10 rebounds. On January 25, 2014, he recorded a career-high 27 points against Michigan. In 35 games, he averaged 16.7 points, 4.0 rebounds, 2.7 assists and 1.8 steals in 32.3 minutes per game.
On April 14, 2014, Harris declared for the NBA draft, forgoing his final two years of college eligibility.
On June 26, 2014, Harris was selected with the 19th overall pick in the 2014 NBA draft by the Chicago Bulls. He was later traded to the Denver Nuggets on draft night. On July 31, he signed his rookie scale contract with the Nuggets after averaging 18.6 points, 4.2 rebounds, 2.6 steals and 2.0 assists in five Summer League games for the team. After missing the first seven games of the 2014–15 season due to a back injury, Harris made his NBA debut on November 14 against the Indiana Pacers. In 18 minutes of action, he recorded 13 points, 3 rebounds, 2 assists, 2 steals and 1 block in a 108–87 win. He did not manage to eclipse that scoring total for the rest of the season, tying his season high of 13 points in the second last game of the season against the Los Angeles Clippers.
In July 2015, Harris re-joined the Nuggets for the 2015 NBA Summer League. On October 11, the Nuggets exercised their third-year team option on Harris' rookie scale contract, extending the contract through the 2016–17 season. He earned the Nuggets' starting shooting guard spot for the 2015–16 season, going on to score a then career-high 20 points on November 20 in a loss to the Phoenix Suns. Harris missed a string of six games between November 28 and December 8 due to a concussion he suffered against the San Antonio Spurs on November 27. He returned to action on December 11 against the Minnesota Timberwolves, starting in his 17th game of the season and scoring 12 points in a 111–108 win. In the following game on December 14, Harris scored a career-high 21 points in a 114–108 win over the Houston Rockets. He tied that career high on December 22, scoring 21 points in a loss to the Los Angeles Lakers. Harris had another 21-point effort on March 4, 2016 in an overtime loss to the Brooklyn Nets. In 2015–16, Harris was just one of seven players to average 12+ points, shoot 47% from the field, 35% from three, and 81% from the free throw line. During the 2016 off-season, he was part of the USA Men's Select Team, a team selected to train with the USA Basketball Men's National Team in preparation for the 2016 Rio Summer Olympics.
In July 2016, Harris re-joined the Nuggets for the 2016 NBA Summer League. On October 5, 2016, he was ruled out for four to six weeks with a partially torn right groin. On October 21, the Nuggets exercised their fourth-year team option on Harris' rookie scale contract, extending the contract through the 2017–18 season. He missed the first four games of the 2016–17 season with the groin injury, but upon returning to action in early November, he sustained a foot injury after just five games. He was subsequently sidelined for up to four weeks. In his first game back on December 15 after missing 16 straight, Harris scored 18 points in a 132–120 win over the Portland Trail Blazers. Four days later, he scored a career-high 24 points in a 117–107 win over the Dallas Mavericks. On February 24, 2017, he set a new career high with 25 points in a 129–109 win over the Brooklyn Nets. He bested that mark on March 8, 2017, scoring 26 points in a 123–113 loss to the Washington Wizards. On March 20, 2017, he set a new career high with 28 points in a 125–124 loss to the Houston Rockets.2012 Indiana Mr. Basketball
2012 Jordan Brand Classic game invitee
2012 Indiana Gatorade Player of the Year
2012 Indiana All-Star
2012 Indiana-Kentucky All-Star series MVP
2012 First-team Parade All-American
2011 Indiana Junior All-Star
2011 All-Hoosier Cross Roads Conference
2011 Indianapolis Star First Team honoree
2011 Hamilton County Player of the Year
2011 Hoosier Basketball Magazine All-State selection
Harris is the son of Gary and Joy Harris (née Holmes). Joy was a four-year letterwinner at Purdue from 1987 to 1991, and currently ranks seventh in school history with 1,747 points; a 1991 first-team Kodak/WBCA All-American, she went on to play in the WNBA for the Detroit Shock in 2000.