The appointment of Khosrowshahi, who described himself as "a fighter", comes as Uber is trying to recover from a series of crises that culminated in the ouster of its former CEO Travis Kalanick in June.
The back-and-forth has also featured interjections from people loyal to Mr. Kalanick who are seeking Benchmark's removal from the Uber board.
Uber is also under federal scrutiny for use of its so-called Greyball tool, secretive software for evading local authorities in cities where the service isn't yet legal.
But if Uber wants to remain a disruptive force in the transportation industry a decade from now, some investors believe it needs a visionary CEO who isn't afraid of taking risks.
But she reportedly had a list of demands conditional to her becoming Uber's next chief.
"The most surprising element of this story - to me, anyway - is that Meg Whitman was in contention for the CEO role at Uber up until the very last minute".
DOMINIC LORRIMER Uber asked all its app users for permission to collect the post-trip location data but only collected it from Android devices
Don't expect Huffington to grill Khosrowshahi, of course, although I am guessing she will lob in a devastating query about his sleep habits.
But of the three candidates, Khosrowshahi, 48, may well be the best suited to steer Uber in the months and years ahead.
"Desperation sometimes drives innovation", he told the publication.
Immelt is leaving GE after spending 16 years at the company and his departure date is set to be on 31 December 2017, although his successor John Flannery will take over at the start of August.
Mayer was Yahoo's CEO before Verizon completed its acquisition of the company.
Earnings figures confirmed by AFP showed that adjusted net revenue was $1.75 billion in the second quarter, more than doubling from about $800 million in the same period in 2016.
"Indeed, it has appeared at times as if the search was being manipulated to deter candidates and create a power vacuum in which Travis could return", said Benchmark in an open letter to Uber employees.
He inherits at Uber a high-stakes lawsuit filed by Alphabet Inc's Waymo that threatens Uber's self-driving auto business, a board divided by one investor's lawsuit against Kalanick, and an organization struggling to overcome allegations of sexual harassment and executive misconduct. The failures led to a 2014 data breach that exposed the names and license numbers of thousands of Uber drivers.