She has since become the focus of a worldwide media frenzy, with the press describing her as a "femme fatale".
Alex Chapman met Anna in 2001, at a London party. Five months later they were married in Moscow, but moved back to the UK in 2002. They divorced in 2006 but apparently remained close friends.
Chapman said his former wife had told him during their marriage that her father had been high up in the ranks of the KGB.
"Her father controlled everything in her life, and I felt she would have done anything for her dad," he told the Telegraph.
"When I saw that she had been arrested on suspicion of spying, it didn't come as much of a surprise to be honest."
The couple visited her father, Vasily Kushchenko, in 2002 in Zimbabwe, where he was working as a diplomat.
Chapman described Kushchenko as a "scary" man who "didn't trust anyone".
"He would never introduce me to other Russian people who came to the house and he always seemed to have a lot more security than the other diplomats," he said.
Alex Chapman said his wife changed during their marriage from a carefree woman living a "bohemian" lifestyle to an "obnoxious" and money-obsessed person.
"When she was still living in London she fell in with a group of people who had a lot of influence. She would go to film premieres and became arrogant and obnoxious, always going on about powerful people she was meeting," he said.
After their marriage broke down, Anna moved back to Russia, Chapman said, "but then all of a sudden she wanted to go to America.
"She started seeing a very rich American guy who took her to the States and, when she came back, she said she loved it".
Chapman said he was surprised because his ex-wife had previously made disparaging remarks about the US and has said she did not want to go there.
He told the Telegraph how her business, an internet estate agency, appeared to be going very slowly and then "what in the space of what seemed a few weeks she was employing 50 people and the business was flourishing".
"Clearly a lot of money had been pumped into the business from somewhere, but I couldn't work it out," he said.
The Telegraph said British intelligence was now investigating whether Anna Chapman had worked as a spy when she lived in Britain or was recruited when she lived there.
She was remanded into custody without bail at a New York court on Monday.