The former Liverpool midfielder made the comments following Sunderland’s 3-0 victory over Hull City at home in the Premier League at the weekend.
Anichebe scored twice for the Black Cats to help them to all three points at the Stadium of Light last Saturday afternoon.
The 28-year-old Nigeria international striker, who joined Sunderland in the summer transfer window, also scored in the 2-1 victory over Bournemouth away from home at the Vitality Stadium in the league just before the international break.
Redknapp has praised Anichebe, and has claimed that the former Everton striker has transformed the way Sunderland play.
“Victor Anichebe has given Sunderland a focal point and going with two up front has transformed the way they play,” Redknapp wrote in The Daily Mail. “So many struggling teams set up with a 4-5-1 and play negatively because they are scared to lose.”
“Anichebe is an old-fashioned battering ram of a forward,” added Redknapp. “He is the kind of goalscorer that Hull and Swansea, their rivals in the bottom three, are lacking.
“Jermain Defoe is going to score even more with Anichebe alongside him. Before Anichebe returned to the side I gave Sunderland no hope of survival. It is so crucial they keep him fit and hungry.”
Sunderland are still in danger of getting relegated to the Championship at the end of the season, but back-to-back wins against Bournemouth and Hull have given them a fighting chance of retaining their Premier League status for the 2017-18 campaign.
David Moyes’s side are second from bottom in the league table at the moment with eight points from 12 matches.
The Black Cats are three points behind 17th-placed West Ham United and will take on Liverpool away from home at Anfield in the Premier League on Saturday afternoon.