The impressive 26-year-old, who made the PFA's Championship team of the season, was told he needed the operation midway through the campaign but put it on hold in a bid to aid the club's ultimately unsuccessful bid for promotion.
Johnson missed just one league match this season despite various injuries, with his only absence coming after taking a severe blow to the throat from Crystal Palace's Claude Davis which left him in hospital until the morning of April's home encounter against Burnley.
He will be fit in time for next season but where he will be plying his trade remains to be seen with a host of Premier League clubs believed to be interested in acquiring his services, most notably Sunderland and Middlesbrough.
Meanwhile, chairman Peter Ridsdale has admitted Cardiff cannot suffer a huge financial loss on Joe Ledley after the midfielder turned down the offer of a new deal.
"Joe is out of contract during the summer of 2010 and we can't allow ourselves to get into a position where he could walk away from Cardiff City at the end of next season," said Ridsdale in the Western Mail. "Our offer is still open for us to sit down for talks on a new contract."