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.
"Elliot is a young player who we've been aware of for some time. He's hugely talented and has been known to Lee Clark at Fulham.
"We hope that, like Ryan Bertrand, we can bring him on as a talent, so that he returns to his club a better player."