Last month, Saatchi, 70, was photographed choking Lawson, 53, on a restaurant patio. Controversy erupted after the photos were published online, as fans and commentators condemned the shocking behavior.
Saatchi initially made a public statement calling the choke hold that brought Lawson to tears part of a "playful tiff." Domestic violence victims' advocates were outraged at his response.
Saatchi later accepted a police caution for assault, but said he had only done so to stop the incident from "hanging over" them.
Lawson has made no comment since the incident. She has moved out of their shared home and rented an apartment with her 17-year-old son, Bruno.
Saatchi then made an extraordinary statement saying he would seek a divorce, claiming he would end the marriage because she had refused to defend him. He said he had "clearly been a disappointment."
But Lawson, who was not aware of his intentions before they were published, ended up filing the divorce papers.
Lawson is represented by her first cousin, the Baroness Fiona Shackleton, who has represented Paul McCartney and advised Prince Charles during his divorce.
Saatchi reportedly dispensed with lawyers to deal with Shackleton himself, hoping to keep his multimillion-dollar art collection intact.
The couple are estimated to be worth more than $225 million, and reportedly signed a prenuptial agreement. After a hearing lasting just one minute, a "quickie divorce" was granted by decree nisi, which will be followed by a finalizing decree absolute in six weeks.