Lee Bullock has also left Ninian Park this summer, joining
The Bluebirds remain some £30m in debt, with a wage bill of an estimated £6m.
Key players have already left Cardiff oin recent times with top striker Rob Earnshaw leaving last August, while club captain Graeme Kavanagh left before the end of the season to join Wigan Athletic.
"When fit, Thorney was undoubtedly the leader of our line, a tremendous player in every sense," said Hammam.
"I believe a lot of Rob Earnshaw's success here was down to his partnership with Thorne.
"But our manager has a different idea of how he wants our front line to work, a different style of approach.
"Thorney is also easily the biggest earner at the club. We've got plenty of big earners, but he's at another level again.
"To get players in we have to get players out.
"We have to change because the team has stood still, clearly it wasn't a team that was going to get us promotion."
Speaking about his move to Norwich Thorne said:
"I'm really excited by the move, it's a great opportunity," Thorne told the Canaries' website.
It is believed that Hammam is also considering a 3.2m bid for defensive duo Danny Gabbidon and James Collins.
With the money much needed, and captain Gabbidon, one of the club's highest earners and desperate for a Premiership move, it is inevitable that he will leave, however, Hammam had previously said that he would sell one of his "untouchables" of which Collins is one.