Belgian Clement was sacked on Sunday the day after a home defeat by St Mirren, the Buddies first league win at Ibrox in more than 30 years, left second-placed Rangers 13 points adrift of rivals Celtic in the standings.
The 47-year-old Ferguson, who won five league titles, five Scottish Cups and five League Cups across two spells at Ibrox, previously served as caretaker coach of Blackpool in 2014.
He has also managed Clyde, Kelty Hearts and Alloa Athletic.
"I want to wish Philippe every success in the future," Rangers CEO Patrick Stewart said in a statement. "He is a fine man whom I have enjoyed working with in my short time here so far."
"I also want to welcome Barry back to the club. We appreciate him and his team stepping into the role at this difficult time."
Clement has guided Rangers to the Europa League last 16, where they face Fenerbahce next month, but they were knocked out of the Scottish Cup by second-tier Queen's Park this month and lost the League Cup final to Celtic on penalties in December.
"I want to reiterate, the issues we are facing run deeper than the manager," added Stewart. "The ongoing football review seeks to address those issues and we will continue to implement its findings in the coming weeks and months ahead of appointing a new, permanent manager."
Former boss Steven Gerrard, ex-Everton manager Sean Dyche and Derek McInnes, currently in charge at Kilmarnock, have been linked with the vacancy.
19°C