Vanhaezebrouck was dismissed after Anderlecht lost 2-1 at newly-promoted Cercle Brugge in mid-December, their third defeat in four league games. They had also been knocked out of the Europa League and the Belgian Cup.
"We are appointing Rutten in order to achieve great success this season and in the seasons to come," Anderlecht sporting director Michael Verschueren said on the club's website.
Rutten, 56, left Israeli side Maccabi Haifa in November and has also coached Al Shabab, Feyenoord, Vitesse Arnhem, PSV Eindhoven, Schalke 04 and FC Twente.
Anderlecht, the most successful side in Belgian club football, are fifth in the country's top division, 14 points behind leaders Genk.