A group of institutional investors with more than $31 trillion invested in the U.S. stock market is starting to get corporate buy-in for its governance guidelines.

Prudential Financial Inc. is one of the first companies to embrace the Investor Stewardship Group’s principles on corporate governance by voluntarily reporting on how the company follows them. The group, whose members include BlackRock Inc., the Vanguard Group and 58 others, had called on companies to provide such disclosures starting in 2018.

“When you engage as much as we do, you know the questions shareholders are asking,” said Peggy Foran, who leads Prudential’s corporate...