Obscure Commons rules mean that Tony Blair cannot simply resign as MP for Sedgefield in order to take up his new position as Middle East envoy.
Instead, he has to go through the little-known process called "taking the Chiltern Hundreds".
Signing the papers permitting Mr Blair to quit parliament was Mr Brown's last act as chancellor of the exchequer.
Under a procedural device dating back to 1623, members of parliament cannot directly resign their seat. In those days, serving in parliament was often regarded as an obligation, rather than an honour or a privilege, and it was thought necessary to dissuade people from leaving Westminster.
Any MP who wants to quit must go through the process of applying for a paid office of the Crown, which automatically disqualifies him or her from holding a seat in the Commons.
Two such offices are used for this purpose - crown steward and bailiff of the Chiltern Hundreds and of the Manor of Northstead. An MP wishing to resign applies to the chancellor for one of the offices, which he or she keeps until the chancellor appoints another applicant or until the holder applies for release from it.
One of Mr Blair's predecessors as Labour leader, Neil Kinnock, took the Chiltern Hundreds in 1995 in order to take up a post as European Commissioner, and Peter Mandelson became steward of the Manor of Northstead in 2004 for the same reason. - (PA)
"The Rt Hon Tony Blair MP had an audience of the Queen this afternoon and tendered his resignation as Prime Minister and First Lord of the Treasury, which Her Majesty was graciously pleased to accept. Mrs Blair was also received by the Queen.
"Her Majesty received in audience the Rt Hon Gordon Brown MP and requested him to form a new administration. The Rt Hon Gordon Brown MP accepted the Queen's offer and kissed hands upon his appointment as Prime Minister and First Lord of the Treasury. Mrs Brown was also received by Her Majesty."