It had been in talks with stadium operators the London Legacy Development Corporation (LLDC) for six months over a naming-rights deal.
But a Vodafone spokesman confirmed the company has "no plans to sponsor the London Stadium".
A stadium spokesperson said they were still "actively seeking a naming rights partner".
"Interest remains high within the market and we are confident we will find the right partner," they said.
Vodafone has reported an annual loss of £5.2bn but denied this was a factor in its decision.
A raid by HM Revenue and Customs (HMRC) officials on West Ham's offices last month was also ruled out as a reason for the company to pull out, sources at the club and Vodafone have said.
It is understood talks ceased because Vodafone did not think the range of events at the stadium where the 2012 Olympic Games was held was attractive enough for marketing purposes.
The venue can only host a limited number of events because of its use as a football ground, although the World Athletics Championships and several concerts will be staged there this summer.
This is the second time a sponsorship deal at the £750m stadium has faltered.
Indian conglomerate Mahindra had been in talks with the LLDC last year.
West Ham are unlikely to see any direct benefits from a sponsorship deal as under the tenancy arrangement, the LLDC take the first £4m a year from any naming-rights contract.

The teenager was a passenger in a Fiat Punto which crashed with a Mini Cooper near Cockermouth.
The 18-year-old driver of the Punto and the 23-year-old Mini driver are both in a serious condition in hospital, Cumbria Police said.
The road between Tallentire and Gilcrux was closed from 17:15 GMT until midnight.
Telecoms company Vodafone has pulled out of a £20m deal to sponsor West Ham's London Stadium home.
[NEXT_CONCEPT]
A 17-year-old girl has died and two men were seriously injured after a Christmas Eve car crash in Cumbria.