Aldridge, 36, is 6-foot-11 and was forced to retire at the end of last season because of a heart scare. He has since been cleared to resume playing again.
“I retired in April based on what I believed was the wisest precautionary decision for my personal health at the time, but further testing and evaluation by several top physicians has convinced the doctors, myself and the Nets that I’m fully cleared and able to return to the rigors of the NBA,” Aldridge told ESPN in a statement.
“I loved my brief time with Brooklyn and am excited to rejoin the team in pursuit of a championship.”
He will join a crowded frontcourt that not only includes Kevin Durant, but also Blake Griffin and new signee Paul Millsap. If healthy, Aldridge may be able to find minutes by playing some center, something he had done previously.
He appeared in just five games with the Nets, averaging 12.8 points and 4.8 rebounds. That run followed a 21-game stint and contract buyout with the Spurs late in the season.
Johnson, 25, is 6-7 and appeared in 18 games and averaged 5.2 points and 5.0 rebounds.
“Since he was on a three-year, minimum-salary contract, Johnson can’t be claimed off waivers using the minimum salary exception, but a team with a trade exception big enough to absorb his non-guaranteed $1.76MM salary could submit a claim,” wrote Dana Gauruder of Hoops Rumors. “If he goes unclaimed, Johnson will become an unrestricted free agent on Sunday.”