Scott Licastri, 22, will however have to pay £100 compensation to the owner of the cat and also muzzle his one remaining dog when out in public.
Licastri had been walking his dogs during the afternoon of March 31 when they had chased a cat into a garden and attacked it, the court heard on Friday. The owner, Mr Knight, attempted to get the dogs off , and the cat, a five year old called Dexter, had died about a week later from its injuries.
The court heard the vet bill for the cat came to £1,400, and although Mr Knight was insured, there was a £100 excess to pay.
Licastri, of Neville Road, Gargrave, who admitted to being in charge of a dog dangerously out of control, apologised to Mr Knight at the time, and came forward following a press appeal.
He had since sold one of the dogs and had made arrangements for the other one, called Billy, to be kept with a farmer friend.
Magistrates told Licastri they understood it was the nature of Lurchers to run after animals and gave him an absolute discharge, although he would have to pay compensation and keep the dog muzzled in future. He was also ordered to pay costs of £85.