Vaughan announced his decision yesterday following the series defeat at home to South Africa, and Paul Collingwood also revealed that he wanted to step down as captain of the one-day side.
Pietersen is one of the favourites to take over both jobs, with Andrew Strauss and Andrew Flintoff also in contention.
And Atherton insists it is the South Africa-born Pietersen who should be given the chance to lead his adopted country.
''If you're talking about someone to take on both jobs then Kevin Pietersen becomes the number one candidate because he's one of the few people who can be guaranteed their place in both teams,'' he told Sky Sports News.
Atherton also suggested that Collingwood may have been pressured into quitting the one-day role as England look to revert back to a single captain.
''Michael Vaughan's decision is his own decision, but I can't believe that Paul Collingwood made that decision off his own back,'' he said.
''Clearly they want to unite the job and get one bloke in there, and they've given Paul a gentle nudge to say that this is in the best interests of the team.'' Atherton was sympathetic of the pressures that moved Vaughan to step aside.
''He's been a wonderfully successful captain, England's most successful in terms of Test match wins, and is surely one of
England's greatest ever captains. In terms of playing, captaining, leading, decision-making, Michael Vaughan is the best man for the job.''
''I know what he's been going through. It's a wonderful job but it's also a job that becomes all-consuming. He said he's not been himself at home and wanted to 'get back to being me','' he added.
''When you're supposed to be at dinner with friends or the wife, you're thinking about who should be opening the bowling the next day and how to tell your mate he's not in the next team.
''That pressure eventually bears down on you and if you're not getting runs as well then it becomes very difficult.'