The 48-year-old agreed a one-year-deal with the Rotterdam-based club and will start work on Monday assisted by former team-mates Jean Paul van Gastel and Giovanni van Bronckhorst.
He won the European Championships with Netherlands in 1988 and finished his international career with 78 caps and 14 goals.
Koeman, whose older brother Erwin coached Feyenoord from 2005 to 2007, played for the club from 1995 to 1997 when he hung up his boots and pursued a career as a coach with Vitesse Arnhem, Ajax Amsterdam, Benfica, PSV Eindhoven and Valencia.
In May 2009, Koeman joined AZ Alkmaar but he only lasted just over six months and was sacked in December.
Koeman has guided Ajax and PSV to the domestic title and after taking up his post with Feyenoord will have played and managed the three biggest Dutch clubs.
Feyenoord, UEFA Cup winners in 2002, finished a lowly 10th in the 18-team top flight last season are recovering from a financial crisis with debts of 40 million euros.
