Al Maghrabi had snatched Rana as she played outside her home in the Yemeni capital Sana'a during the festival of Eid.
He took her back to his father's home where he raped and then strangled the toddler with his bare hands.
Muhammad al Maghrabi, 41, was shot at point blank range with a machine gun being convicted by a Sharia court in Yemen of raping and strangling three-year-old Rana al-Matari.
Safaa's father Muhamad said he had contacted Rana's family after seeing al Maghrabi's execution in the same public square last month.
Mr al Almatari said justice had been served by the summary execution in accordance with the law of the land.
He told Mail Online: 'Justice and the ruling of God and Sharia law have prevailed.
Speaking exclusively to Mail Online after witnessing the brutal execution the toddler's father said: 'I feel as if I have been reborn. I am relieved now.' Other family members had gathered with a crowd of thousands screaming 'long live justice' as al Maghrabi was dragged from the back of a police van.
The mother of a four-year-old girl who was raped and murdered today told of their joy at the execution by machine gun of their daughter's killer.
Safaa al-Matari's parents said justice had been done as the little girl's father spoke of his 'happiness' that the murderer had been punished in 'spectacular way'.
It is believed the killer's family, who lived two doors away from the Almatari family, tipped off police about their son's involvement.
The dead girl's mother Jamileh fainted when she was told her body had been found in an empty shop and was rushed to hospital where she was treated for shock.