The Belgian has signed a three-and-a-half year contract at Ibrox. Michael Beale was sacked earlier this month with Rangers trailing Celtic by seven points at the top of the Scottish Premiership.
"I am honoured to have been appointed as the new manager of Rangers. I am hugely excited by this chance to achieve success at one of Europe's most iconic clubs across four competitions in what remains of this season and beyond," said Clement in a club statement.
Clement won three consecutive Belgian titles in charge of firstly Genk and then Club Brugge between 2018 and 2021. The 49-year-old then had a spell at Monaco between January 2022 and June this year but left after finishing only sixth in Ligue 1 last season.