Goldsmith pleaded guilty to one count of assault by beating.
The attack happened at 1.30am after the couple had returned by taxi from a charity auction at Home House, a private members' club in central London, on October 13.
Gary, who is worth nearly $40 million, attended both Kate, 35, and sister Pippa's weddings.
Mrs Goldsmith asked the Mr Shepherd to call the police, while the court heart that Goldsmith was "aggressive" to the taxi driver.
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Julie-Anne was knocked down to the pavement outside the couple's home after Goldsmith assaulted her, according to taxi driver Daniel Shepherd, who reported the incident to the police after driving the two home.
Westminster Magistrates' Court heard that Goldsmith - who is the younger brother of Kate's mother Carole Middleton - left Julie-Ann Goldsmith unconscious outside of their London home.
'They both got out of the taxi and he (Mr Shepherd) describes Mrs Goldsmith slapping her husband to the face, ' she said.
Goldsmith will be sentenced at the same court on November 21. Gary admitted he pushed his wife hard with his left hand, but denied using a hook. "He says "She appears to be unconscious, she isn't moving".
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It carries a maximum penalty of six months' imprisonment.
Chief Magistrate Emma Arbuthnot said: "I am excluding custody and looking at a community order".
Goldsmith married his first wife Miranda Foote in 1991 and reportedly bought a luxury five-bedroom house in Maidenhead, Berkshire complete with a pool. Their mother worked in a shop and also did accounts, while their father was a painter and decorator.
After he and Luan divorced, he married Julia Leake following a whirlwind romance.
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In 2005, he sold his shares in Computer Futures for £17million and bought a villa in Ibiza and called it "La Maison de Bang Bang". She met husband Michael at the airline and they later had Kate and Pippa.