Murray has signed a two-year contract with the Kirkcaldy club after missing out on promotion with Airdrie following the defeat to Queen’s Park in the Championship play-off final.
The former Hibs and Rangers player replaces John McGlynn, who left Stark’s Park at the end of the season to take over the reins at Falkirk.
Murray departs Airdrie after four years in charge having finishing runners-up to Cove Rangers last season following a 23-game unbeaten run.
He previously managed Dumbarton and St Mirrren and had a spell as assistant boss at Norwegian side Asker.
"Ian is a creative hardworking ambitious manager, with an ability and foresight to make changes at the appropriate time, coupled with his determination to win, I feel we have made a great appointment and look forward to Ian bringing success to Raith Rovers.”
A Raith statement added that it hoped the 41-year-old’s appointment represented "the turn of the first page in a new chapter in the club's history after proving himself as the outstanding candidate in an extremely strong pool of interviewees for the role."
McPake meanwhile has penned a two-year deal at East End Park, replacing John Hughes, who stood down last week following the club’s relegation to League One.
The 37-year-old steered Dundee to promotion via the play-offs in season 2020-21 but was sacked in February with the Dens Park side sitting second bottom of the Premiership.
McPake said: “I’m delighted to have been appointed manager at such a prestigious club within Scottish football. It`s been a challenging year for the club but I am excited and optimistic about how we can build the club up and get it moving in the right direction from League One.”
Pars chairman and CEO David Cook added: “We had a clear idea of what we were looking for in our new manager and we feel James fits the bill very well.
"League One is a clear reset moment for the club and from our conversations with James, it is clear we share the same drive and ambition to help build the club up.”