Allardyce was confirmed as Roy Hodgson’s successor with the national team on Friday, leaving a Premier League vacancy at the Stadium of Light.
A statement published on Sunderland’s official website on Saturday morning revealed Moyes, 53, has arrived on Wearside on a four-year contract as chairman Ellis Short’s “first choice” to take control of the Black Cats.
“I have taken over a big British club, with a great support and I’m looking forward to working in the Premier League again.
“I look forward to continuing the good work done by Sam.”
Moyes had been on Sunderland’s radar when they looked for a replacement for Dick Advocaat last October and, while his stock may have fallen since ill-fated spells at United and then Real Sociedad, his 11 years at Everton made him an attractive proposition and Black Cats chairman Short was thrilled to have secured his long-standing top target.
“We are absolutely delighted to welcome David Moyes to Sunderland, who was by far and away our first choice,” the American businessman said.
“He is a man whose football pedigree speaks for itself and is someone I have long admired.
“I have spoken with him on many occasions and I have always been hugely impressed. He was my number one managerial target for the last five appointments, but his desire to honour existing contracts meant we were not able to bring him to Sunderland previously.
“To be able to finally welcome him as our manager is fantastic news for the club.
“The fact that David has committed to a four-year deal is a clear demonstration of his belief in what he can achieve here.
“It is our aim to become a better, stronger and more stable football club and with a manager of David’s calibre and experience at the helm, we have a fantastic opportunity to begin looking upwards, rather than downwards every season.”
Moyes has managed more than 800 senior games in club football and boasts a wealth of top-level experience.
The Scot began his managerial career with Preston in 1998, before moving to Goodison Park in 2002 and overseeing a largely positive tenure which ended when he succeeded Sir Alex Ferguson in the United hotseat ahead of the 2013-14 season.
He signed a six-year contract at Old Trafford but was sacked after just 10 months, with the Red Devils seventh in the Premier League.
A fresh challenge in Spain followed, in November 2014, but he lasted only a year in the role.
“I am delighted to have joined Sunderland,” Moyes said on www.safc.com. “I am relishing the challenge and excited by the opportunity.