Providence Equity Partners LLC agreed to sell scuba certifier Professional Association of Diving Instructors to a group of wealthy families and endowments for more than $700 million, according to people familiar with the matter.

The consortium includes philanthropists who were drawn to PADI’s efforts to promote oceanic conservation as well as its business, people familiar with the deal said. They purchased the company through an entity dubbed Mandarinfish Holding, named for a Pacific Ocean-dwelling fish whose vivid orange,...