The former Newcastle United and West Ham United boss has been given the role at the Stadium of Light on a two-year contract.
Allardyce will replace Dutchman Dick Advocaat, who left the Premier League outfit earlier this month.
Former Sunderland star Gray is delighted to see Allardyce take charge of the first team and hopes that the club gets some stability under him.
Delighted with our new appointment. Now for some stability at the football club. Best of luck Big Sam #safc— michael gray (@mickygray33) October 9, 2015
Former Manchester United and Everton star Phil Neville made the following post on Twitter and added on Breathesport.com: "Brilliant appointment by Sunderland - a proven premier league manager who will bring stability to a club that needs strong leadership."
Brilliant appointment by Sunderland - a proven premier league manager who will bring stabi... . http://t.co/RHaQSGqXrk— Philip Neville (@fizzer18) October 9, 2015
Sunderland are second from bottom in the league table at the moment with just three points from eight matches.
The Black Cats will take on West Bromwich Albion away from home at The Hawthorns in the Premier League after the international break.
It will not be easy for Sunderland to retain their Premier League status for next season, but Allardyce specialises in keeping clubs in the top flight of English football.