Details of the contracts announced Thursday were not made available.
Cooley, a 6-foot-9, 246-pound Notre Dame product, signed his deal after back-to-back 10-day contracts. He's played in six games and averaged 1.7 points. He was first signed from the D-League's Idaho Stampede, where he averaged 16.8 points, 12.5 rebounds and 1.3 blocks in 20 games.
The 6-6, 201-pound Johnson averaged 7 points, 1.5 rebounds, 1.5 assists and 1.5 steals in two games while playing with the Jazz on a 10-day contract earlier this year.
The Jazz also waived guard Ian Clark on Thursday. He played in 23 games with the Jazz and averaged 1.9 points.