The club are down in sixth place in the league following Saturday's 1-0 home defeat by Platanias, a result that cost Spaniard Fabri his job.
Panathinaikos are three points behind fifth-placed PAS Giannena and need to finish in the top five to contest a mini-league which decides European places for next season.
"It is a great honour that the club has put its faith in me during this difficult period," the 52-year-old Vonortas told reporters on Monday.
"It is a considerable challenge for any coach to lead Panathinaikos and I am a man who likes challenges. I love Panathinaikos and want to help the club as much as I can for what is a difficult mission."
Vonortas is the fourth coach of the season at the Greek club, following Jesualdo Ferreira, Juan Ramon Rocha and Fabri.
He is a former Panathinaikos player and has previously coached the academy side and worked as an assistant to Rocha.
"The final three matches of the season are vital and we are trying to fight for something which is out of our hands and does not depend solely on our results," Vonortas added.
"I believe we have enough quality and I think we still have every chance of getting to the playoffs."
Fabri's fate was sealed after he launched a stinging verbal attack on the players following Saturday's defeat.
The 57-year-old, well known for his animated touchline antics and sharp comments during his time in Greece, suggested some of his squad "did not have the balls" to wear the shirt.
Arch-rivals Olympiakos Piraeus have already wrapped up the title and Panathinaikos are 35 points behind after experiencing their worst season on record.
The club's previous worst performance came in 1980-81 when they collected only 13 victories. This season the Greens have picked up nine wins.