Wright's new contract is a one-year deal that pays him $1.5 million and makes him a free agent next year. Last year, he signed a five-year, $35.8 million deal that supposedly had $15 million guaranteed.
His four-game suspension last year eliminated the guarantee on his second-year base. He was scheduled to make $7.75 million this year. Because that salary was no longer guaranteed, the Bucs could threaten to cut him if he didn't take a pay cut.
Wright started 10 games last season, finishing with one interception, seven passes defensed and 39 tackles.
With the Wright pay reduction, the Bucs now have $32.9 million of cap room, second most in the league.
The team announced Wright's restructured one-year deal on Tuesday but didn't disclose terms.