Anichebe, who made more than 130 appearances under Moyes at Everton, said his relationship with the Scot had tipped the scales in favour of joining the Black Cats.
"He (Moyes) brought me through as a young player and was a big factor in me coming here," the striker told the Sunderland website (www.safc.com).
"I had a few options in England and Europe but the manager was a huge pull for me. He knows me inside out and I feel like he can get the best out of me."
The Nigeria international was released by West Bromwich Albion in July after failing to score in 14 appearances in all competitions last season. He played 55 times for the club.
(Reporting by Simon Jennings in Bengaluru; editing by Ken Ferris)
