"We have engaged in a partnership with Rutten in order to achieve great success this season and in the following seasons," the club said in a statement late on Sunday.
Rutten, 56, will start his duties on Monday and travel with the squad to Spain for winter break training, it added.
Predecessor Hein Vanhaezebrouck was dismissed last month after a series of poor results that led to Anderlecht's exit from the Europa League and poor run in domestic first division where they are currently fifth.
Anderlecht next play Ghent on January 20.
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Rutten played his entire career at Dutch side Twente and has one Dutch cap. He has managed a number of Dutch clubs, including PSV Eindhoven and Feyenoord, German side Schalke 04 and, most recently, Israel's Maccabi Haifa.
(Reporting by Philip Blenkinsop)
