Muslic led Cercle Brugge to an eighth-placed finish in Belgium’s top flight in his first season in charge.
Last season he improved on that as they finished fifth in the regular season before guiding them to fourth place in the end-of-season play-offs.
That saw them reach this season’s Uefa Europa League qualifying rounds in which they beat Kilmarnock over two legs before being knocked out by Norwegian side Molde and dropping into the Conference League.
He was sacked at the start of last month with Cercle in the relegation play-off places following a loss at bottom-of-the-table Beerschot.
Muslic is the fourth permanent manager of Argyle in 13 months.
Steven Schumacher, who led the Pilgrims to the League One title in 2023, left the club in December of that year to take over as Stoke City boss.
He was replaced by former England youth coach Ian Foster, but his three-month tenure saw the Pilgrims drop into the relegation zone, and it was director of football Neil Dewsnip and Nancekivell who guided the side to safety on the final day of the season.
Former England skipper Rooney took over in the summer, but he could only manage four league wins in his half-season in charge which ended on New Year’s Eve with the club bottom of the Championship and with the worst defensive record in the English Football League.