She will become senior vice-president of policy and communications at the taxi company, which is expected to list on the stock market this year and has been valued at as much as $50bn (£31.7bn).
Whetstone will replace David Plouffe, who was Barack Obama’s campaign manager in 2008 and joined Uber in August last year.
He has been elevated to the role of chief adviser to the company and its chief executive Travis Kalanick, and will also sit on the board of Uber.
Whetstone’s appointment was first reported by Recode. She begins her new job next month.
In recent months Uber has been buffeted on several fronts in a number of cities and countries by regulators, taxi drivers and others who oppose the rise of the smartphone-based service that has proved popular with thousands of users.
In the face of fierce resistance in numerous European cities, Kalanick said in January that he wanted to focus on forging “new partnerships”. Uber’s expansion could eventually create 50,000 jobs, he added.
Policy Exchange, a conservative British thinktank, said Hilton would become a visiting scholar and visit the UK several times a year but not be based in London.
Before starting her career with Google in Europe in 2005, Whetstone was Michael Howard’s chief of staff after he became Conservative leader in 2003.
She joined Conservative Central Office after studying politics at Bristol University before switching to Carlton Communications – where she worked with David Cameron – and then went on to co-found the PR agency Portland.
The couple were godparents to Ivan, the Camerons’ disabled son who died in 2009.
In March Whetstone wrote a blog post for Google hitting back at Rupert Murdoch’s News Corp after the Wall Street Journal accused Google of wielding undue political influence. Robert Thomson, chief executive of the company, had accused Google of creating a “less informed, more vexatious level of dialogue in our society”.
Whetstone wrote: “Given the tone of some of your publications, that made quite a few people chuckle” and followed the comment with a gif of a baby laughing.
This article was written by Chris Johnston, for theguardian.com on Thursday 14th May 2015 00.20 Europe/Londonguardian.co.uk © Guardian News and Media Limited 2010