The 64-year-old Dutchman has agreed a one-year deal starting after the European Championship in which he leads Russia in a group along with hosts Poland, Czech Republic and Greece.
"We wanted a top coach for coming season and Advocaat saw perspective in PSV," said technical manager Marcel Brands.
"He is looking forward to work with assistants he also coached as players in the past [Philip Cocu and Ernest Faber] and we are sure we made the right choice as he rejected very lucrative financial offers from Russia."
Advocaat had a previous spell at PSV from 1995-98 during which they won the Dutch league title and cup, joining the club after leading the Dutch national team to the 1994 World Cup quarter-finals.
Advocaat then joined Scottish club Rangers, winning a domestic treble of trophies in 1999 and double a year later.
Advocaat coached the Dutch team again from 2002-04, reaching the Euro 2004 semi-finals and in 2006 he joined Zenit St Petersburg whom he led to the Russian title in 2007 and the UEFA Cup the following year.
In 2010 Advocaat accepted his another job as a national coach with Russia, after previous spells with United Arabic Emirates, South Korea and Belgium.
PSV finished third in the Dutch league after sacking coach Fred Rutten in March, failing to qualify for the Champions League for the fourth year in a row.
