Saudi Arabia’s sovereign-wealth fund bought a stake Sunday in a firm owned by billionaire Prince al-Waleed bin Talal, further intertwining the government with a high-profile investor who was once detained by the state over corruption allegations.

The Public Investment Fund agreed to pay Prince al-Waleed $1.51 billion for 16.9% of Kingdom Holding Co., a figure based on the closing price on the last trading day before the transaction was announced, according to a filing with the Saudi stock exchange.