The striker left the Gunners for Manchester City in 2009 and has signed for the White Hart Lane club until the end of the season.
"There is always aggravation when players leave clubs but he will get on and hopefully play well," said Redknapp. "William Gallas played against Arsenal last year and for me was the man of the match. He showed his character last year in that game and I am sure Manu will do the same on Sunday.
"It is another great opportunity for Emmanuel Adebayor to play for Tottenham. He has been playing well for us, the crowd love him and he has been a big bonus for us so far. His performances have been fantastic. Let's hope he can keep that up."
Spurs are currently in sixth place in the Premier League, while Arsenal occupy 12th position.