The Belgian has been handed a three-and-a-half-year contract with the Ibrox club and comes in as a replacement for Michael Beale, who was sacked at the start of this month.
Beale's dismissal came after Rangers lost three of their opening seven league matches of the season.
Clement is the 19th permanent manager in Rangers' history and starts his reign with a home game against Hibernian next weekend.
The 49-year-old has won league titles as a manager in Belgium with Genk and Club Brugge and his most recent club was AS Monaco, whom he led from January 2022 to the end of last season.
"I am honoured to have been appointed as the new manager of Rangers Football Club and I'd like to thank the board for giving me this opportunity," he said after his appointment was confirmed.
"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.
"I am looking forward to meeting with the players in the coming days and to meeting our supporters at next Saturday's home match with Hibernian, as we set out together to create a successful, winning Rangers."
The Rangers chairman, John Bennett, added: “I would like to offer my warm congratulations to Philippe as he becomes our 19th manager. His appointment comes at the end of a carefully planned and comprehensive recruitment process.
“A team led by our CEO James Bisgrove, members of the board, and former Rangers player and manager Graeme Souness, has spent the last 10 days interviewing several high calibre candidates, with those individuals undergoing a rigorous interview and vetting process. We thank all candidates for their interest in the position.
“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.”
