Johnson, 26, was scheduled to be paid a base salary of $9.069 million in 2019 on the fifth-year option in his rookie contract. The Texans save that full amount on their salary cap with the move.
He was placed on injured reserve last season after suffering a concussion in a Week 1 loss to the New England Patriots. It was his second concussion in less than a month, as he also left Houston's preseason game against the San Francisco 49ers on Aug. 19 after hitting his head on the field.
He told the Houston Chronicle that he has been medically cleared by neurologists to return.
"They told me I'm cleared, good to go and I'm in great shape moving forward," Johnson told the newspaper. "I'm feeling good. I'm going to be ready to go next season."
Johnson played in 35 games for the Texans, making 18 starts. He has an interception, 14 passes defensed and 122 tackles in four seasons.
"Kevin has had some tough luck the last few years," general manager Brian Gaine said last week.
Johnson will test the free-agency market, but the Texans could bring the cornerback back on a cheaper contract if he does not sign elsewhere.
ESPN's Sarah Barshop contributed to this report.