The 42-year-old would start work next week after agreeing to an 18-month contract with an option for an additional year, the club announced.
"With Sunday, Fortuna is choosing a trainer who is young and ambitions, who has a vision and who the players will look up to," club chairman Isitan Gün said in a statement.
"We are seeking someone who can combine attractive football with the pure will to win. In Sunday, we think we have found this coach."
Sittard fired Ben van Dael 11 days ago as they dropped to third from bottom in the standings on 15 points from 19 games.
Oliseh was briefly coach of Nigeria, quitting in February after just eight months after claiming he had not been paid his salary.
The Nigerian has also served as technical director at Eupen in Belgium, where he has lived since ending his playing career.
As a player, Oliseh had stints at FC Cologne and Borussia Dortmund in Germany, Juventus in Italy and Ajax Amsterdam, and won an Olympic gold medal with Nigeria in 1996.
While European coaches head to Africa regularly, many of them untested and searching to kick-start their careers, there has been little traffic in the other direction.
The only other African-born coach currently plying their trade at a first or second division club in a major league in Europe is former Angola international Lito Vidigal.
The 47-year-old, who was born in Luanda but raised in Portugal, is in charge of Arouca, who are 12th in the Portuguese top flight.
Africa's only major international coach was Mozambique-born Mario Wilson, who managed Portugal from 1978-80 and had three spells in charge of Benfica.
(Reporting by Mark Gleeson; Editing by John O'Brien)
