Stefanovic has signed a two-year contract at Carrow Road and joins for an undisclosed fee, while Omozusi has arrived on a season-long loan.
Norwich boss Glenn Roeder is happy with his double signing.
Roeder said: "It's great to bring in two players with Premiership experience and their arrival is part of our squad rebuilding ahead of the new season.
"Stefanovic is a player I tried to sign when I was with West Ham, after he first caught my eye at Vitesse Arnhem. I couldn't afford him then, but have a second opportunity to work with him now and I am very much looking forward to it.
"We hope that, like Ryan Bertrand, we can bring him on as a talent, so that he returns to his club a better player."