The Grizzlies also announced Friday that they have waived guard Marquis Teague.
Brooks originally signed a 10-day deal with the Grizzlies on March 27, and he averaged 23.3 points with 3.7 assists coming off the bench in three games. The 6-foot-5, 200-pound guard scored 70 points, the most by any player in franchise history over his first three games.
The 29-year-old Brooks also became only the second Grizzlies player to average at least 20 points a game in his first three games.
Johnson, 28, has averaged 16.6 points, 6.4 rebounds and 1.6 assists this season in 44 games with the Memphis Hustle, the Grizzlies' G League affiliate. The 6-9 forward also was shooting 41.7 percent (136 of 326) from 3-point range for the Hustle.
Teague appeared in three games for the Grizzlies as a reserve. He averaged 3.7 points, 4.3 assists, 2 rebounds, 1.3 steals and 24.7 minutes.