The law bans mandatory payments from employees to the unions that represent them under collective bargaining agreements.
The American Association of University Professors-American Federation of Teachers Local 6075 ratified the agreement earlier this month, and the Wayne State board of governors followed suit Wednesday.
The vote was along party lines on the Democratic-controlled board. The Republican-led state Legislature has threatened retaliation against schools that adopt long-term contracts not covered by the right-to-work law.
Republican Gov. Rick Snyder said Wednesday he doesn't have a problem with longer contracts as long as they're "fairly bargained" in an "arms-length basis."