Advocaat revealed the news to Dutch football magazine Voetbal International on Monday, just hours after Poyet was relieved of his duties following Sunderland's 4-0 Premier League drubbing at the hands of Aston Villa over the weekend.
The 67-year-old Dutchman, who spent four months as head coach of the Serbia national team last year, told VI: "I am now in a dark hotel, but soon I'll be working in the Stadium of Light."
Advocaat's move to Sunderland marks his first role in the Premier League, having spent time in the Netherlands, Germany and Scotland.
And the well-travelled Dutchman is tasked with preserving Sunderland's top-flight status, with the embattled club just one point above the relegation zone after 29 matches.
Advocaat will get his first taste of Premier League football against West Ham on Saturday.
"This is something I always wanted to do, the Premier League. The Premier League is a phenomenal competition," Advocaat told AD Sportwereld.
"As a manager that is where you want to work, that has such a pulling power.
"Saturday, West Ham awaits. And then there's the international break. And then – the derby with Newcastle United.
"That is really something to look forward to because believe me, this just is a very big club."
