Papers released by the court said Madonna petitioned for divorce on the basis of Ritchie's "unreasonable behavior," but did not elaborate.
Judge Phillip Waller ruled that he did not need to apply family law in the case - meaning that he accepted an agreement reached by the couple over their assets and children.
Neither appeared at the brief court session, in which "Ciccone M L v Ritchie G S" was one of 17 cases given a preliminary decree. The divorce can become final after six weeks and a day,.
British news media reported, without identifying the sources of their information, that the couple had reached a settlement that would see the pop superstar keep the majority of her estimated 300 million pound ($445 million) fortune and share custody with Ritchie of their two children: Rocco, 8, and David Banda, 3, who was adopted from Malawi in 2006.
Madonna has a 12-year-old daughter, Lourdes, from a previous relationship with personal trainer Carlos Leon.
Requests for comment from representatives for the couple were not returned.
An agreement on terms would avert an expensive courtroom battle like the one between former Beatle Paul McCartney and model Heather Mills. Mills has said the media coverage of the rancorous divorce had pushed her to the brink of suicide; McCartney compared the process to going through hell.
Madonna and Ritchie, director of "Snatch" and "Lock, Stock and Two Smoking Barrels," married in December 2000 at Skibo Castle in the Scottish Highlands.
Madonna and Ritchie announced last month they were divorcing. They own homes in London, Los Angeles and New York, and a 1,200-acre (480 hectare) retreat in England.