Johnson grew up in Spotsylvania County, Virginia but moved to Woodbridge, Virginia to be closer to Bishop O'Connell High School after he enrolled at the school. He entered high school at 5'6, but grew six inches by his senior year. He became Bishop O'Connell's starting point guard as a junior and was named second team All-Washington Catholic Athletic Conference (WCAC) after averaging 10.5 points, 4.2 rebounds and 3.4 assists. Johnson was named the (WCAC) Player of the Year, as well a first team All-State and first team All-Metro by The Washington Post, as a senior after averaging 18.4 points, 4.0 rebounds and 4.3 assists per game. Rated the 39th-best point guard prospect in his class by ESPN and a three-star recruit by 247Sports, Johnson originally committed to play college basketball at the University of Nebraska over Georgetown and Georgia Tech. Johnson requested that Nebraska release him from his National Letter of Intent in the spring of his senior year after the departure of the assistant coach who recruited him. He ultimately committed to play at the University of Pittsburgh.
As a freshman, Johnson led the Panthers with 15.5 points and 4.5 assists per game while also averaging 3.9 rebounds and 1.3 steals per game and was named to the Atlantic Coast Conference (ACC) All-Freshman team. He was the first Pitt freshman to lead the team is scoring since 1985 and was the only player in the ACC to average at least 15.0 points and 4.5 assists per game.
Going into his sophomore season (2019–20), Johnson was named the 75th-best collegiate basketball player by CBS Sports and the 51st-best prospect for the 2020 NBA draft by ESPN. Johnson scored 13 points in the Fort Myers TipOff against Kansas State, with four points coming in the last ten seconds to help secure a 63–59 win. He scored 20 points with six rebounds and six assists against North Carolina on January 18, 2020 to help close out the Panthers' first-ever season sweep of UNC. Johnson finished the season with 11.7 points, 4.9 assists, 3.7 rebounds and 1.8 steals per game. As a junior, he averaged 14.2 points, 5.7 assists and 3.4 rebounds per game.

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