The 33-year-old, who has 31 Scotland caps, came through Hibs' youth ranks before joining Rangers in 2007.
Hibs head coach Neil Lennon described the signing as a "coup" for the club promoted to the Premiership last term.
Whittaker told Hibs' website: "When I decided to return to Scotland, Hibs was the club I hoped to come to."
The Edinburgh-born defender fell out of favour under fellow Scot Alex Neil at Carrow Road last season as Norwich failed to make a swift return to the Premier League.
And he returns to the club with whom he won the Scottish League Cup in 2007.
"While the discussions have taken a while, they have always been positive and I am very pleased to be back playing at Easter Road for the Hibernian fans and I hope I can play my part in ensuring a successful return to the top flight," Whittaker added.
However, he will not be available for Saturday's opening League Cup game against Montrose on Saturday as he requires international clearance.
Lennon told BBC Scotalnd: "He is a player I admired for a long time, even playing against him when he was a young lad.
"We have got him at a very good age, he's still only 32, and he is very versatile.
"He adds to the experience and quality we have.
"The squad is still thin and the striking position is the priority now."
Meanwhile, Hibs face competition from clubs abroad if they wish to sign Wales striker Simon Church.
The 28-year-old has been on trial with the Easter Road club along with former Liverpool winger Jermaine Pennant.
Church is a free agent after a hip injury ruined his spell at Dutch Eredivisie club Roda last season and is considering offers from overseas clubs.
He spent half a season on loan at Hibs' Premiership rivals Aberdeen during the 2015-16 campaign.
Church, previously with Reading and Charlton Athletic, scored six goals in 13 starts for the Pittodrie outfit but was released on his return to MK Dons and subsequently made only four starts for Roda.
Pennant, 34, who has also been on the books of Arsenal, Birmingham City, Real Zaragoza and Stoke City, ended last season on a short-term contract with English League One outfit Bury, making seven appearances.
Steven Whittaker has returned to Hibernian on a three-year contract following the right-back's summer release by Norwich City.