The prime minister, Boris Johnson, and his estranged wife Marina Wheeler are preparing to end their marriage after reaching an agreement over money.

A family court judge on Tuesday approved a financial settlement and gave Wheeler permission to apply for a divorce decree which will bring the marriage to an end.

Neither Johnson nor Wheeler, a barrister, were at the 10-minute private hearing in the central family court in London but both were represented by lawyers.

Johnson is believed to be the first prime minister to be divorced in office in modern times.

Judge Sarah Gibbons oversaw the hearing, which was listed as “Wheeler v Johnson”, in private. Members of the public were barred but the judge said journalists could attend.

She said Johnson and Wheeler could be named in reports but said no detail relating to money could be revealed. Detail of the settlement was provided to the judge in writing by lawyers. The terms were not aired at the hearing.

Wheeler and Johnson, who have four children, separated in 2018 after marrying in 1993.

Johnson, 55, has been dating Carrie Symonds, 31, since last year and the couple live together in Downing Street. Johnson and Wheeler announced that they had separated, and were going through the divorce process, in September 2018.

Judge Gibbons gave Wheeler the go-ahead to apply for decree absolute, a divorce decree which will end the marriage “out of time”. Rules say applications for a decree absolute must be made within 12 months of the granting on an initial divorce decree, a decree nisi.

Applicants have to tell a judge why there has been a delay if an application is made outside that 12-month period.

Wheeler was represented by Lucy Stone QC at Tuesday’s hearing. Johnson was represented by solicitor Neil Russell, who is based at law firm Seddons.

Johnson was a childhood friend of Wheeler – the daughter of the BBC journalist Charles Wheeler – when both were pupils at the European School in Brussels.

Johnson met his first wife, Allegra Mostyn-Owen, while they were students at Oxford. They married in 1987, but the marriage was annulled in 1993.

Johnson is thought to be the first serving prime minister to feature at such a family court hearing.

The Duke of Grafton was granted a divorce, by act of parliament, while serving as prime minister in 1769.

Johnson has repeatedly come under scrutiny over his personal life. Appeal court judges ruled in 2013 that the public had a right to know that he had fathered a daughter during an adulterous liaison while mayor of London in 2009.

In 2004, he was sacked from the Tory frontbench over a reported affair with the journalist Petronella Wyatt.