The list, topped by Scottish first minister Nicola Sturgeon identifies women who have had an "exceptionally large impact".
Keeping Up with the Kardashians' star Jenner, formerly known as Bruce, is at number seven.
She revealed her transition to Caitlyn on the cover of Vanity Fair last month.
The former Olympian, whose famous children include step-daughter Kim Kardashian and daughter Kendall Jenner, is honoured for bringing the experience of being a trans woman to a global audience.
Both the Vanity Fair photoshoot and the ensuing #CallMeCaitlyn hashtag adopted by many fans on Twitter generated huge publicity.
Actress, director and humanitarian campaigner Jolie made number three on the list, which was revealed on BBC Radio 4, for "using her celebrity to impressive ends" and the "Angelina-effect".
The term was coined after the actress revealed her genetic predisposition to breast and ovarian cancer, sparking other women to seek out testing.
Jolie has spoken openly about her double mastectomy and having her ovaries and fallopian tubes removed to prevent cancer.
The Guardian's first female editor Katherine Viner was at number four on the list, just weeks after taking up the job, while Wintour, editor-in-chief of American Vogue, was at number two.
Whistles chief executive Jane Shepherdson, who was on the judging panel, said the editor "influences the world in what to wear, how to look, and who to celebrate.
"Like the captain of almost any other industry, Wintour's word is almost law."
The list was counted down during a special Woman's Hour show from the BBC Radio Theatre, hosted by presenters Jane Garvey and Jenni Murray.
The panel of judges, headed up by journalist and broadcaster Emma Barnett and including human rights lawyer Helena Kennedy QC and Radio 1 DJ Gemma Cairney, looked at well-known women's personal ability to influence others.
Sturgeon is at number one following the Scottish National Party's performance in this year's general election, winning 56 our of 59 possible seats in Scotland.
Though she didn't stand as a candidate, the judges called Sturgeon "the woman of the moment in terms of influence and hard power".