The Michael Morton Act would compel prosecutors to share case files with defense attorneys that can help defendants' cases.
It is named in honor of Michael Morton, who spent 25 years in prison after being wrongfully convicted of killing his wife. The district attorney in his case, now a Texas judge, is facing charges he deliberately withheld evidence from Morton's defense.
The proposal sailed through the Senate and House and has been applauded by Perry.
During Thursday's ceremony, the governor will also address reporters - even as lawmakers from both parties scramble to reach a deal to finalize the Texas budget.