They ordered the man, Mr Tombe, to pay a dowry of 15,000 Sudanese dinars ($50) to Mr Alifi.
"We have given him the goat, and as far as we know they are still together," Mr Alifi said.
Mr Alifi, of Hai Malakal in Upper Nile State, told the Juba Post newspaper that he heard a loud noise around midnight on 13 February and immediately rushed outside to find Mr Tombe with his goat.
"When I asked him: 'What are you doing there?', he fell off the back of the goat, so I captured and tied him up." Mr Alifi then called elders to decide how to deal with the case.
"They said I should not take him to the police, but rather let him pay a dowry for my goat because he used it as his wife," Mr Alifi told the newspaper.