South African-born Pietersen had been backed for the role by pundits including Geoffrey Boycott but was regarded as less likely to be given the job than either Paul Collingwood, the favourite, or Andrew Strauss.
Pietersen said in a statement that he did not feel ready to take on the additional responsibility involved in captaining his adopted country.
"At this stage in my career I don't think it is the right time for me," he said. "I thought about it long and hard but right now I am happy playing and supporting the team like that.
"I would be humbled in the future to be given the opportunity to captain my country but right now I don't think it is the right time for me."
"Whoever gets the job (when the team is announced) tomorrow (Friday) will get my full support. It is a new era now with a new coaching staff and a good time for England to move forward."
Pietersen, who has informed England coach Peter Moores and the selectors of his decision, recognised that whoever gets the captaincy has a huge job on their hands to turn around England's fortunes in the one-day game.
He believes England neglected the form of the game under former coach Duncan Fletcher.
"It is a very, very big job. Ever since I have been playing in one-dayers, for almost the last three years, we have not won too many trophies," he said.
"The one-day scene has been neglected. It has been more of a Test match environment. The schedules we play now are hard with Test match after Test match and then jumping into the one-dayers it can be a bit of a release.
"But we have to turn that around now because the World Cup wasn't the best of months for us. It is massive now that everybody buys into winning and a successful campaign with the one-day team. It will be a heck of a job."
Boycott had said the England selectors would be "chickens" if they did not name Pietersen as captain when the squad for the West Indies series is announced tomorrow.
"Geoffrey has been very supportive and I thank him for that. It is fantastic to know that greats of the game are supportive," added Pietersen.
"In the future it would be an amazing opportunity to captain my country. It would be an enjoyable ride. At the moment I am enjoying everything I have got now. It is very complimentary what he has said but don't think it is the right time now."
Pietersen believes Vaughan made the correct decision in standing down as captain and effectively calling a day on his one-day international career.
"Vaughan is a great leader. I think he has done it with the best interests of the country," he said. "I think if he wants to prolong his career and win the 2009 Ashes as captain for all of us it was a good decision.
"With the current schedule your bodies take an absolute hammering day by day. He has got a crooked knee and let's hope it goes on for another two years in Test cricket."