Stewart also scammed at least five other victims with his false claims of wealth between January 2009 and January 2011.
He told one woman he could offer her work as an interior designer earning a total of $800,000 over three years.
Stewart also told a husband and wife that he was a former Goldman Sachs partner and could employ them as a captain and cook on his yacht.
He appeared at the Old Bailey to plead guilty to one count of fraud on a "full facts basis".
Stewart has recently been staying at The Priory, the private mental health hospital famous for treating celebrities.
Prosecutor Ben Maguire said: "Mr Stewart paid for his admission with the use of credit cards. This is a man who is on benefits and we are not aware how he can afford the costs of the Priory, at £4,000.
"That is a concern we are investigating at the moment."
Judge Stephen Kramer QC remanded Stewart in custody until his sentencing on December 19.
The judge told him: "The fact that I am asking for these reports should give you no illusions, all sentencing options are open and the almost inevitable conclusion would be a sentence of immediate custody."
Outside court Mr Maguire said: "This man is a sophisticated conman. He managed to persuade this poor lady he was a billionaire financier with Goldman Sachs who had started his own fund.
"He groomed her over about six months. She fell in love with him and sent him one million dollars. He then funded a lifestyle that he was a billionaire."
DS Mick Richards of the Economic Crime Unit at Sussex Police said: "He was living in a bedsit on benefits in Burgess Hill.
"He spends his life on the internet conning people and he struck lucky."
Stewart received the money from Ms Siegenthaler on September 27, 2010, but had spent almost all of it by January 2011.
In June this year he denied seven counts of fraud, two of converting criminal property, two or removing criminal property and one of transferring criminal property.