The signing of the 31-year-old is a relief for Sunderland manager Steve Bruce whose side have tumbled to 13th in the league after a bright start.
"He's a big, strong, powerful centre forward and one we've been tracking for a long time," Bruce told the club's website (www.safc.com).
"I'm delighted we've been able to bring him to the club, he'll bring another dimension to our striking options."
Benjani arrived in English football at Portsmouth in 2006 before being signed by former City manager Sven Goran Eriksson for around 7.5 million pounds in 2008.
However, with City's attack now boasting Carlos Tevez, Emmanuel Adebayor and Roque Santa Cruz, his first-team opportunities have been severely restricted.
Sunderland, without a league win for two months, also signed Tottenham Hotspur right back Alan Hutton on loan.
