The 60-year-old has signed a two-year contract and will take over at the Stadium of Light with immediate effect.
Allardyce said: “I have enjoyed my break from football and now I’m raring to get back. I met with Ellis and we spoke at length about the club and his ambitions and I knew I wanted to be part of that. I hope to be able to help to bring the stability and success that everyone wants.
“Of course it’s a challenging job, but it’s something I have experience of in the past. I’m looking forward to working with the players and of course I will be relying on the help of the Sunderland supporters, whose tremendous passion I have experienced first-hand. I can’t wait to get started.”
“I am very pleased to welcome Sam to our football club,” Sunderland chairman Ellis Short said on the club’s official website.
“Sunderland is a club he knows well and he was the obvious best choice for the job. He has vast experience of managing in the Premier League and an understanding first-hand of the north east and the passion of our fans, which will stand him in great stead.
“I would like to assure our fans that once Dick made us aware of his intention to leave, Lee Congerton oversaw an organised and structured recruitment process, that bore very little resemblance to what has been described in the media.
“For example, this was a very popular job, proactively sought after by a large number of managers – contrary to much of what has been portrayed. The process was made easier by the fact that Sam was such an obvious choice.
“The other misconception is that Sam had to be persuaded to join us; nothing could be further from the truth. From the very beginning, he understood the importance of this job and showed great enthusiasm for the role and a desire to be part of moving this club forward.”
