The Leicester City player, who denied the charge, was arrested on 29 December after police were called to reports of a row.
Manchester Magistrates Court heard Simpson, 28, was found with his "hands around the throat" of his ex-partner at a house in Worsley, Greater Manchester.
"All sentencing options, including custody, remain open," said the judge.
Ex-Newcastle and QPR full-back Simpson, from Eccles, Greater Manchester, will be sentenced next month.
Simpson and Stephanie Ward - the mother of his child - had been out for a meal in Manchester city centre hours after he played in Leicester's 1-0 victory over Hull City in the Premier League on 28 December.
The court was played an eight-minute 999 call with sounds of a struggle and the pair arguing.
PC Gareth Hughes told the trial he arrived at the scene to hear "choking" and found Simpson "straddling" Ms Ward with "his hands firmly placed around her neck".
In his evidence, Simpson denied assaulting Ms Ward, and said the row started over old text messages and moved on to him buying her expensive shoes for Christmas.
"I didn't think she deserved she shoes," he told the court. "She was on the sofa and I was trying to get them off her."
Ms Ward, who gave an account to officers at the scene, later withdrew her statement and did not support the prosecution.
Manchester District Judge Alexandra Simmons rejected Simpson's account as "unworthy of belief".
She added: "I take the view this is a serious matter, aggravated by being in domestic context. I take the view it does pass the custody threshold. She is vulnerable because of the personal context and to strangle someone is akin to using a weapon."