The Cardiff City chairman added a clause in Prior's contract which also states that he must eat both the brain and the testicles of a sheep, along with a raw liver still swimming in blood.
"It's simple," explained Hammam. "With Spencer being non-Welsh, he needs to prove to the people of Wales that he understands the place - then he can become a true leader.
"Everybody knows that the Welsh shag sheep - if he's not going to shag sheep, then nobody will trust him here.
"We gave him two to choose from - either Dolly, she's a black sheep, or Mimi, who is white. He chose Dolly.
"The biggest problem was with his wife. She wasn't too keen at first, but I explained to her that there was no emotional attachment involved and that it was purely a physical thing. We gave him an inflatable sheep to take home so that he can improve his technique."
When asked if the club encouraged relations with sheep directly before matches, the former Wimbledon chief responded by saying: "We're strict disciplinarians here. One hour before and after matches, sheep-shagging is strictly forbidden. We are actually very conservative!"
Turning to more serious matters, he revealed that the fans of Cardiff City played an important part in securing Prior's signature.
"We hounded him, you see. Welsh fans are not just mad, they are insane! They kept phoning him and his family - we bombarded him with calls.
"I can't tell you how delighted I am to have him here. We need him to inject a bit of experience into a squad that already has seven Welsh Under-21 internationals in it.
"He has agreed to take a massive gamble as he was on Premiership wages. He has almost taken a 50 percent pay cut, but I've told him that we will more than compensate for that once we reach Division One."
Prior could well be joined at Ninian Park by another new signing after Hammam also revealed that he is hopeful of finalising a deal with Stoke City midfielder Graham Kavanagh.
"Hopefully he will be a Cardiff City player by tomorrow night. He's travelling over from a holiday in Ireland as we speak and he'll have a medical tomorrow.
"Then it should be a case of just dotting the i's and crossing the t's."
Having secured the signature of Prior, Hammam is obviously a happy man, although he did conclude by admitting that there was still one thing bothering him.
"Our only real concern is that the EU may have a problem with Spencer's contract. That shouldn't be too difficult though, because Neil Kinnock is very influential there and, as a Welshman, he also shags sheep!"
