The 62-year-old will replace his fellow Dutchman at Alkmaar for the rest of the season while continuing with his national team job, the club said.
"We need to get European football at AZ," Advocaat said in a statement issued by the club. "If we do not achieve this, then I will have done something wrong."
Alkmaar sacked Koeman on Saturday after a series of poor results. His team won the Dutch Super Cup but failed to reach the Champions League knockout phase this season and recorded their seventh loss in 16 league games on Friday.
Advocaat was appointed Belgium coach two months ago after a spell at Zenit St Petersburg, the team he led to the Russian league title in 2007 and the UEFA Cup the following year.
He took up the Belgium job three months earlier than planned after being sacked by Zenit following some disappointing results.
Combining the Belgian and AZ positions will be made easier for Advocaat by the fact that the country is playing only friendlies until the end of the season. Belgium have failed to reach the 2010 World Cup finals.
AZ had approached Advocaat in the summer to become their coach but because he had already agreed to take the Belgium job, he declined to consider the Alkmaar position, Advocaat told Dutch football magazine Voetbal International earlier this year.
