One in and one out for Pompey
The 30-year-old keeper was disillusioned following last week’s arrival of David Forde on a season-long loan.
Now he has negotiated an exit with 12 months remaining on his contract in favour of a switch to Norwich.
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Hide AdThe Championship club have already signed Northern Ireland keeper Michael McGovern this summer to challenge John Ruddy.
Jones has also made the Carrow Road move, following 64 appearances for Pompey since arriving in the summer of 2014.
Meanwhile, Cook will now complete a deal for Hunt, who has spent the past three weeks training with the Blues.