Gallas wearing the armband appeared unthinkable when he crossed the north London divide this summer.
Redknapp said: "I spoke to Luka about it and he's fine; he gets on and just wants to play.
"When Dawson and Tom Huddlestone are back, we'll look at it again.
"I'm a bit superstitious so I just thought, it went well at Arsenal and he responded, so we're delighted he is captain."
Gallas has now skippered all three of London's biggest clubs and Redknapp believes this speaks volumes for the 33-year-old's leadership, adding: "(It is) unusual to captain Chelsea, Arsenal and Spurs."