The 28-year-old has signed a two-year deal with the Canaries after his contract with Melbourne Victory expired.
Gunn revealed Norwich beat off competition from several clubs for Theoklitos' signature.
"Michael has always been the number one target this summer, so obviously I'm delighted he's put pen to paper." Gunn told the club's official website.
"Although other clubs were interested in trying to sign Michael he wanted to come and play for us and that is the kind of passion and commitment to Norwich City which I'm looking for in my players.
"Michael came for a few days with us in March and myself, Paul Crichton, and in fact everyone at Colney were very impressed with both his goalkeeping and also his personality. He will be a massive presence both on the pitch and in the dressing room."