During the summer of 2019, Satoransky left Washington and signed a three year contract with the Chicago Bulls. The versatile guard appeared in all possible 65 games for the Bulls, with 64 starts, during the pandemic-shortened 2019-20 season. Satoransky averaged 9.9 points, 5.4 assists, 3.9 rebounds and 1.2 steals in 28.9 minutes per contest. He shot 43.0 percent from the field, 32.2 percent from three (with 1.0 three-pointer per game) and a career-high 87.6 percent from the free-throw line. On Nov. 6, the Czech play-maker scored a career-best 27 points, plus added eight dimes, seven boards, four three-pointers and a steal during a win at Atlanta. On Jan. 6, during a loss at Dallas, Satoransky dished a career-high 14 assists, to go with 11 points, five boards and a steal. For the season, Satoransky had three double-doubles. The guard posted 11 games with at least 15 points, 22 games with at least five rebounds and 21 games with at least seven assists. He also had 10 games with at least three steals. Satoransky led the Bulls in assists per game and free throw percentage (minimum 5 games played). In the eight games that Satoransky played at least 35 minutes, he averaged 13.4 points, 7.8 assists, 4.9 rebounds, 1.5 three-pointers and 1.9 steals per contest.

For the second year in a row, Satoransky saw his workload increase with the Wizards. Satoransky unexpectedly started 54 of the 80 games in which he played during the 2018-19 season. The increased workload resulted in career highs nearly across the board for the former 32nd overall pick. Satoransky's role truly opened up in late December after John Wall was lost due to injury. As the new starting point guard, Satoransky posted 10.7 points, 6.2 assists, 4.3 rebounds and 1.1 steals per contest over his 54 starts. On Jan. 11, the Czech guard delivered his first career NBA triple-double. Satoransky achieved the feat with 18 points, 12 boards and 10 dimes in a home win over the Bucks. That effort marked the start of a seven-game hot streak in which he boosted his average production to 13.7 points, 7.3 assists, 5.7 rebounds and 1.9 steals. All told, he recorded 10 games with 10 or more assists and seven double-doubles. Satoransky also shot an impressive 40 percent from behind the arc. He made a season-high four 3-pointers on seven attempts as part of a 20-point, four-rebound, six-assist game Dec. 29 against Charlotte.

In his second NBA season, Satoransky saw increased playing time at point guard as John Wall dealt with knee issues and missed 41 games. Satoransky appeared in 73 games for the Wizards and played 22.5 minutes per night -- nearly 10 more than his rookie campaign. The 26-year-old from the Czech Republic set new career highs across the board with 7.2 points, 3.9 assists and 3.2 rebounds per game. Not surprisingly, he was even more productive as a starter, playing 29.7 minutes per night and finishing with 9.9 points, 5.5 assists and 4.3 rebounds across 30 starts. Satoransky showed a nice shooting stroke all season long, knocking down a career-high 52.3 percent of his shots, including a scintillating 46.5 percent from 3-point range. He made a season-high five 3-pointers on just six attempts against Chicago on Feb. 10 and had seven other outings with multiple 3-pointers. That game against the Bulls was also Satoransky's highest-scoring effort of the season, as he finished with 25 points. He amassed 19 other double-figure scoring games, with 14 of those coming in starts. Satoransky also dished out 10 or more assists three times, recording a high of 11 against the Knicks on Valentine's Day.

Originally a second-round pick of the Wizards in 2012, Satoransky instead chose to remain in Spain, where he was already playing pro ball, until he finally signed with Washington ahead of the 2016-17 season. He appeared in 57 games (three starts) as a 25-year-old NBA rookie, averaging 2.7 points, 1.5 rebounds, 1.6 assists and 0.5 steals over 12.6 minutes per game. The Czech import demonstrated noteworthy positional flexibility, playing shooting guard, small forward, point guard and even a little power forward. In one of his starts, Nov. 12 at Chicago, Satoransky set season highs in both points and assists, scoring 12 while dishing out nine dimes en route to a 106-95 win. He notched his first career double-double in a Jan. 16 win over Portland, tallying 10 points and 10 rebounds with three assists and a steal despite playing only 19 minutes. Satoransky recorded two steals on four separate occasions, showing his ability to make an impact on both ends of the court when given the opportunity.