NBA Commissioner Adam Silver said the move will bring "extraordinary leadership and immediate stability" to the team.
The announcement came after a recording surfaced in which Clippers owner Donald Sterling made racist remarks, prompting widespread outcry.
Last week, Silver fined Sterling $2.5 million and banned him from the NBA for life. He also urged the NBA to force him to sell the team.
In addition to his work with Time Warner and Citigroup, Parsons has also served as a member of President Barack Obama's economic advisory team. He is currently an advisor at Providence Equity Partners.
"Like most Americans, I have been deeply troubled by the pain the Clippers' team, fans and partners have endured," Parsons said after the announcement.