Johnson is available for Wednesday's game against the Bucks, NBA freelance journalist Billy Reinhardt reports.
The Nets signed Johnson to a two-way deal on Tuesday, Adrian Wojnarowski of ESPN reports.
Johnson recorded three points (1-4 FG, 1-3 3Pt), two assists, one rebound, one steal and one block in 15 minutes during Thursday's 123-100 preseason win over the Lakers.
Johnson (finger) was traded to the Suns on Wednesday as part of a three-team deal between Phoenix, Portland and Milwaukee, Adrian Wojnarowski of ESPN reports. The deal also sends Damian Lillard to Milwaukee, Jusuf Nurkic to the Suns, and Jrue Holiday and Deandre Ayton to Portland.
Johnson suffered a right finger injury during Friday's Summer League game against Houston and will not return.
Johnson (finger) is listed as out for Sunday's game against the Trail Blazers.
Johnson closed with 20 points (7-15 FG, 3-7 3Pt, 3-4 FT), six assists and three rebounds in 31 minutes during Monday's 124-90 loss to the Pelicans.
Johnson amassed 12 points (4-9 FG, 1-4 3Pt, 3-3 FT), two rebounds, six assists and four steals across 26 minutes during Friday's 124-96 loss to the Bulls.
Johnson (ankle) will not play in Wednesday's game against the Warriors.
Johnson (ankle) is questionable for Wednesday's game versus the Warriors.