Detective Sergeant Grahme Bartlett, of Queenstown, said the 41-year-old Hungarian man's body was found in Queenstown Bay yesterday afternoon, about 50m from the Queenstown Gardens, in an area not previously searched.
The dive squad had been using sonar equipment to search the lake since Tuesday.
Mr Mudra was last seen paddling a kayak on the lake about 4.45pm last Friday.
The kayak was found about 6pm floating with the paddle and lifejacket both stowed in the cockpit.
The search involved more than 50 people since Friday, including 30 volunteers who had searched the shoreline by foot.
Mr Mudra had been living with his wife in New Zealand for two and a-half years, including 18 months in Queenstown.
The couple had no children.
Det Sgt Bartlett said family in Hungary had been notified.
It was too early to say whether they would be coming to New Zealand.
Police had referred the death to the coroner.
