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,” said Clement in a club statement.
“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.”
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.
His immediate task in Glasgow is to break Celtic’s stranglehold of the Scottish game.
The Hoops have won 11 of the last 12 Scottish Premiership titles and have built up a commanding lead just eight games into the new season.
But Rangers also have the chance of progression in the Europa League despite an embarrassing 2-1 defeat to Aris Limassol in Cyprus earlier this month.
And Clement could quickly get his hands on silverware with his new side facing Hearts in the semi-final of next month’s League Cup.
Rangers are huge favourites to win the trophy with holders Celtic already eliminated.
Club chairman John Bennett confirmed that former Rangers manager Graeme Souness had been part of the recruitment team to interview candidates for the job.
He added: “Philippe proved to be the outstanding candidate across all the key criteria, reinforced by his track record of winning titles and I wish him every success as he leads us forward.”
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