But Vaughan, in a statement issued by the England and Wales Cricket Board (ECB) after close of play on the fourth day of the fourth Test against the West Indies, said he would continue as a one-day international cricketer.
And the ECB also added he would remain England's Test captain.
Vaughan's successor as one-day captain will be announced when the squad for the two forthcoming Twenty20 matches and three limited overs internationals against the West Indies is named on Friday.
However, Vaughan indicated he might miss these matches while the new captain established "his own authority over the team".
Vaughan, who has struggled to reproduce his Test form in one-day cricket, was England's captain at the recent World Cup in the Caribbean where they failed to qualify for the semi-finals.
The 32-year-old Yorkshire batsman said: "Since our disappointing performances in the World Cup, I have been giving careful consideration as to what is the best way forward for the England one-day team and my own role within the side.
"I reached this decision some time ago. But due to intense speculation in the media about my future, I feel it is important to make my intentions clear now.
"Our priority is to build a One-Day squad able to compete strongly at the next World Cup (in Asia in 2011) and I firmly believe that the interests of the team will be best served if I step down and allow another player to gain additional experience of captaincy in the one-day international arena."
He added: "I am committed to continuing as England's Test captain for as long as I can be successful in the role.
"I enjoy the job and I also believe that I will be able to form a strong working relationship with whoever is appointed to the one-day captaincy," said Vaughan, who last month spoke out against a split captaincy.
"It is not my intention to retire from one-day international cricket as a player. I do, however, fully appreciate that the new captain will need a period of time to establish his own authority over the team."
All-rounder Paul Collingwood appears to be the favourite to replace Vaughan as one-day captain, although batsman Kevin Pietersen has also been linked with the job.
Vaughan has yet to score a century in his 86 one-day international appearances, averaging a meagre 27.15 compared to a Test mark of 43.44.
He led England in 60 one-day internationals, winning 32 and losing 22.
At the World Cup, Vaughan scored just 130 runs in England's first eight matches of a tournament where Andrew Flintoff, currently injured, was stripped of the vice-captaincy after a late night drinking session ended in the all-rounder being found in a pedalo in the early hours of the next morning.
Vaughan scored 79 in England's final, 'dead', World Cup fixture against hosts West Indies in Barbados, where neither side had a chance of reaching the last four.
He returned to Test cricket after 18 months out injured, mainly as a result of a longstanding knee problem, with a hundred on his Headingley home ground during England's innings win in May's second Test against the West Indies.
England's 2-0 series clinching victory at Old Trafford completed last Monday saw Vaughan become his country's most successful Test captain with 21 wins in 35 matches.