The 41-year-old former midfielder is currently assistant coach of the Australia national side and will enter his first senior management position after the Socceroos' World Cup campaign.
Van Bommel, who spent seven years with PSV in two spells with the club, succeeds Phillip Cocu, who is moving to Turkish side Fenerbache.
Formerly of Barcelona and Bayern Munich, Van Bommel worked for two years as a youth coach at PSV, winning the national championship last season with the Under-19 side, and has been in line to take charge of the senior squad for some time.
"Because we have our affairs in order, we were able to switch immediately. The scenarios were already ready. Mark was prepped with the youth for the big work," managing director Toon Gerbrands said.
"Moreover, he has international experience as an assistant national coach. Also his World Cup experience is going to help us. We have every confidence in him."