Cunningham has a year left on his contract at Preston and Preston North End can have no qualms with letting the defender move on, having signed him on a free transfer from Bristol City in July 2015.
The 23-year-old becomes the Bluebirds' first new arrival since securing a return to the Premier League.
Murphy was a part of Norwich's massively indifferent season in the Championship last term, as he flattered to deceive on plenty of occasions.
Webber, who spoke to the club's official website following Murphy's move to the Bluebirds, conceded that the academy graduate was looking to leave Norwich this summer.
Josh made his debut for the Norwich during the 2013/14 season before going on to make 108 appearances and scoring 20 goals.
It's always nice when to see one of our own play in the top flight of English football and according to reports we may well have another Irish interest in the Premier League in Greg Cunningham.
"I think he's at the right age now with his best still to come".
The Bluebirds were chasing Irish worldwide Cunningham last summer but couldn't convince Preston to sell, with a move close this time around thanks to Cardiff's promotion to the Premier League.
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