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".
Singer, songwriter and music video director Sia made number six, having written for Beyonce, Rihanna, Jessie J and Katy Perry and achieving solo success with hits like Chandelier.
"It is a secret to most how much of a part of the pop music eco-system Sia actually is," said Cairney, adding, "all the while remaining faceless in an industry so much based on, well, face."
Woman's Hour Power List 2015 - Top 10 influencers
1. Nicola Sturgeon - leader of the SNP
2. Anna Wintour - editor-in-chief of American Vogue
3. Angelina Jolie - actor, director and humanitarian ambassador
4. Katharine Viner - editor of The Guardian
5. Camilla Cavendish - director of Downing Street Policy Unit
6. Sia - singer, songwriter and music video director
7. Caitlyn Jenner - high profile trans woman
8. Karen Blackett, CEO, MediaCom UK
9. Zanny Minton Beddoes - editor-in-chief of The Economist
10. Sara Khan - co-founder of Inspire
Speaking about Jenner's inclusion in this year's top 10, Daily Mail columnist and judge Sarah Vine acknowledged it was controversial, for several reasons.
"Initially... many of us felt that Kim Kardashian would have to appear somewhere - not because any of us felt any particular admiration for the woman, but simply because her influence on millions of women worldwide is undeniable.
"But then the Caitlyn Jenner story broke and I in particular felt that she trumped all others in the celebrity stakes."
She added: "I understand why someone like Jenner might make people feel uncomfortable; but she is a human being like the rest of us and should not be denied the same rights - or indeed respect - as those who live more conventional lives.
"As to her influence, it can only be to the good if a wider audience can learn to understand her experience."
Last year's Woman's Hour Power List, entitled Game Changers, was topped by Doreen Lawrence, while the Queen topped the first list in 2013.
Woman's Hour editor Alice Feinstein added: "The way power operates in today's global, interconnected society is not straightforward - brokers of hard power like prime ministers, presidents and CEOs are no longer calling all the shots.
"What I wanted to examine in this year's list of influencers is how women are operating outside traditional power structures to get things done."
Trans woman Caitlyn Jenner has made this year's Woman's Hour Power List of top 10 influencers, alongside Angelina Jolie, singer Sia and Anna Wintour.