The former Newcastle 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.
The former England international has also explained his earlier claim that Allardyce will not accept the Sunderland job.
Always happens! Sunderland appoint a manager who has them fired up just before the derby. I think Big Sam might want to prove a point!— Alan Shearer (@alanshearer) October 9, 2015
I said unless he has full control and I think you will find, he will have full control! https://t.co/ffibtO3taz— Alan Shearer (@alanshearer) October 9, 2015
Allardyce’s first game in charge of Sunderland will be against West Bromwich Albion away from home at The Hawthorns in the Premier League after the international break. Thereafter the Black Cats will face Newcastle at the Stadium of Light.