The 28-year-old Nigerian international joins the Black Cats on a deal until the end of the season, and becomes manager David Moyes' ninth signing of the summer.
Anichebe told safc.com: “I'm really happy to be here at a great club.
“I have a lot of good friends here and everyone knows that I know the manager really well.
“He brought me through as a young player and was a big factor in me coming here.
“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."