Bobby Roberts was also convicted of failing to prevent an employee from repeatedly beating the animal, which was filmed chained to the ground and being hit with a pitchfork.
Roberts, 69, who ran Super Circus in Polebrook, Cambridgeshire, also failed to ensure the elephant's needs were met, by not giving her medication for her arthritis.
He was given a three-year conditional discharge at Northampton Crown Court but was not ordered to pay costs and was not banned from owning animals.
His wife Moira, 75, was cleared of all three charges by District Judge David Chinery following a five-day trial.
Sentencing, Mr Chinnery said he recognised that Bobby had not directly inflicted the suffering, adding that he had cared for animals ''for the greater part of your seventy years without criticism from any quarter''.
He added: ''As you know only too well there are vast swathes of the public who have publicly voiced their views on what should happen to you.
''No cruelty was administered by your own hand.
''The chaining I regard as serious but the real cruelty it seems to me was inflicted by your groom, a man whom you had entrusted with the care of Anne, behind your back and without your knowledge.
''There are aggravating features identified by the sentencing council, namely the fact that Anne was an animal kept for your livelihood and you were in a position of responsibility.
''Against that there are factors which indicate less culpability, particularly your lack of knowledge.
''As a result of what has happened your business is effectively at an end. You have lost everything which you have built up over the last five decades. I am told that you have no funds at all.''
He added that Bobby had ''suffered enough punishment over the last eighteen months'' and said given his ''exemplary'' past record was not imposing a ban on owning or caring for animals.
The court was shown footage filmed secretly by animal welfare group Animal Defenders International (ADI) of the elephant being kicked and struck with a pitchfork several times by the groom at the circus's winter quarters last year.
The footage, filmed between January 21 and February 15 2011, also showed Anne constantly chained to the ground.
Roberts claimed he was unaware that Anne had been constantly chained and that the groom, who is believed to have returned home to Romania, had not followed his instructions.
He admitted that the elephant would be chained up at times but said his instructions were that she be let loose behind an electric fence in a cordoned-off area.
Following today's verdict, Richard Crowley, deputy chief crown prosecutor at CPS East Midlands, said: ''Bobby Roberts had clear responsibilities for this elephant's welfare, which he wilfully neglected when he treated her appallingly.
''Today should serve as a warning that those who mistreat animals can expect to face prosecution.''