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Mr Benn entered the Commons following a by-election in 1999
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International Development Secretary Hilary Benn will run for the Labour deputy leadership when John Prescott steps down, he has announced.
When Mr Prescott left the job, he would allow himself to be nominated, Mr Benn wrote in a letter to his Leeds Central constituency association.
Mr Benn's parliamentary private secretary Ashok Kumar said his prospects were "looking very good".
Mr Benn is 3/1 favourite with bookmaker William Hill to take up the position.
His father Tony fought unsuccessfully for the same job in 1981.
It is widely assumed John Prescott will quit when Tony Blair steps down
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In his letter, Mr Benn said the party's challenge was in applying "unchanging Labour values in a world that is itself changing fast before our eyes".
"The party will continue to need a deputy leader who offers honest advice and leadership, ensures the voice of the members and affiliated unions is heard in government, works with all colleagues and listens to their views," he added.
The next deputy should carry forward "the fight for social justice and peace in the world, knowing that we achieve most when Labour works alongside the people".
The 52-year-old will need a total of 44 signatures before he can join the race.
Conference announcement
Mr Benn held various middle-ranking ministerial posts before taking up his present job when Clare Short resigned in 2003.
Mr Prescott made clear at Labour's party conference last month that he would be leaving his job.
It is assumed that he will go when Prime Minister Tony Blair decides to move out of Downing Street.
Backbencher Jon Cruddas, Northern Ireland Secretary Peter Hain and Constitutional Affairs Minister Harriet Harman have all said they will run for the post when it becomes vacant.
Commons leader Jack Straw is also expected to throw his hat into the ring.
Education Secretary Alan Johnson is also being tipped to make a bid for the deputy's job.