The 23-year-old had a successful trial at the Premier League outfit and will complete his £1.5million move from South African side Supersports when the transfer window opens in January.
Redknapp said: "I think we've done a deal for him. We're in the process of doing a deal for him.
"He's not expensive. We had him over on trial and we like him.
"He's got potential and we've got a tie up with the club Supersports so we've taken him on."
Khumalo, who was born in Swaziland, scored for his country during this summer's World Cup win over France.
His arrival will be a significant boost to Redknapp, who has seen Michael Dawson join fellow centre-back Jonathan Woodgate on the long-term injury list this season.
Redknapp continued: "It will be a great chance for the kid. He's a great lad. He comes from a poor background and he's desperate for a chance and we're going to give him a chance."