Howden will be replaced by Jonathan Browning who was elected by the British Cycling board, it said in a statement.
The organisation is waiting for the publication of UK Sport's independent investigation into accusations of "bullying" in British Cycling's elite programme.
British Cycling is also at the centre of an investigation by UK Anti-Doping into allegations of wrongdoing.
Howden, together with Team Sky boss Sir Dave Brailsford, went before a Parliamentary committee in December to provide evidence for an investigation into doping in sport.
He was quizzed about the contents of a package delivered by a British Cycling coach to former Team Sky rider Bradley Wiggins at the 2011 Criterium du Dauphine. His evidence, as well as Brailsford's, was later described as 'very disappointing' by UK Anti-Doping chairman David Kenworthy.
Howden, who was re-elected in December, has denied that the move is related to the publication of the report, saying the appointment of former Jaguar Cars managing director Browning was an "important step" in updating the organisation.
One of Browning's first tasks will be appointing a new chief executive after Ian Drake left his post in January.
"British Cycling has delivered tremendous success for the sport at every level over the past two decades, but there is clearly work to do to take the organisation to the next level," he said in a statement.
"Recruitment for a new chief executive is going well and we expect to make a further announcement in the next few weeks."
British Cycling has enjoyed unparalleled Olympic success in the past decade, winning a total of 22 track and road gold medals at the past three Games.
The publication of UK Sport's report is now expected next month, having been delayed.
(Reporting by Martyn Herman; Editing by Hugh Lawson)
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