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Conservative MP Christopher Tugendhat is also giving up his seat to become Britain's second European Commissioner.
The resignation of both men means the delicate balance of the parties in Westminster will not be upset. The government - supported by two Northern Ireland MPs - retains its working majority of one.
No date has been set yet for the two by-elections. It would take a swing of 15% to the Tories for Labour to lose the seat of Birmingham Stechford which Mr Jenkins has represented since 1950.
Mr Tugendhat had a 5,761 majority in his constituency of the Cities of London and Westminster. Peter Brooke, son of Lord Brooke of Cumnor, a former Conservative home secretary, is expected to stand in his place.
According to the tradition of the Commons, MPs cannot resign while parliament is sitting. Instead they have to apply for an office of profit from the Crown, which disqualifies them from being an MP.
Mr Jenkins has written his letter of resignation to the Chancellor and is expected to be given the nominal post of Steward of the Chiltern Hundreds. Mr Tugendhat has sent an identical letter, and is expected to become Bailiff of the Manor of Northstead.
Mr Jenkins will become Britain's first Common Market Commission president. The job comes with an estimated salary of £60,000, which will be topped up with generous allowances for housing, travel and entertainment.
There has been much speculation about how much tax he will pay. EEC officials usually pay a special community income tax which is not more than 25% a year.
He faces a number of serious challenges, on EEC agricultural policy and the farm price review, as well as the politics behind Portugal's expected application to join.
He will also be responsible for who gets what job in the new Commission. There have already been behind-the-scenes negotiations.
A number of British advisers will be going with Mr Jenkins to Brussels, including Crispin Tickell, a Foreign Office career diplomat, Haydon Phillips, who was his private secretary at the Home Office and Graham Avery, an agricultural specialist.
Roy Jenkins' presidency coincided with a renewed challenge from the left-wing of the Labour Party to Britain's continued membership of the EEC.
But he remained a committed European and worked to lay the foundations for the European Monetary System.
He returned to British politics in 1981 as a member of the so-called "Gang of Four" who established the Social Democratic Party.
After initially winning much popular support, the ratings dropped and the party eventually merged with the Liberals to form the Liberal Democrats.
After earning a peerage, Lord Jenkins devoted more time to life outside politics. He became Chancellor of Oxford University and wrote acclaimed biographies of political figures such as Gladstone and Churchill.
He also became a mentor to Tony Blair and commentators have suggested his influence and that of the Social Democrats is reflected in Labour's moderate policies.
He died suddenly in January 2003.
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