Van den Brom leaves Dutch side Vitesse Arnhem to take up the post with the Belgian champions.
Vitesse said in a statement on their website they were "disappointed" that Van den Brom had opted to move to Belgium having been convinced last week that he would stay.
Former Holland and Ajax player Van den Brom, who won two caps for his country, is now 45 and succeeds Ariel Jacobs at Anderlecht. Jacobs resigned earlier this month after delivering the league title.
Anderlecht president Roger Vanden Stock said at a press conference, according to Anderlecht's official website: "I am very pleased that we have quickly found a new coach. We're going to work together for at least the next three years.
"I know that we have been in the habit here of seeing out long contracts, but we have confidence in the qualities of our coach. The future will show us if we are right."
Van den Brom said: "I am very happy to be here as coach, but especially proud that such a great club has thought of me.
"RSCA (Anderlecht) are synonymous with good and attractive football, with a style of play that I appreciate."
Anderlecht are targeting a place in the Champions League next season but begin in the penultimate qualifying round.
"Yes, we all know how important it is for the entire club to take part in this competition," Van den Brom said. "This is a wonderful challenge and we are going to do everything we can to get through these two qualifying rounds."
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