Jonathan Browning, a former chairman of Vauxhall, has succeeded him.
UK Sport was expected to publish a report this month after an independent investigation into the culture and practices at British Cycling - but that has been delayed.
The governing body is also being investigated by UK Anti-Doping over allegations of wrongdoing.
Howden, who was re-elected in December, has denied that the move is related to the publication of the report.
A former managing director of Jaguar Cars, Browning was appointed to the British Cycling board as a non-executive director in March 2015.
"British Cycling has delivered tremendous success 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.
Ian Drake left his post as chief executive officer in January, saying it was the "natural moment" as preparations began for the Tokyo Olympics in 2020.
Browning's appointment comes after a turbulent year for one of the country's most successful and well-funded sports governing bodies.
British Cycling is preparing for the results of the investigation into whether there was a culture of bullying at its world-class performance programme.
Publication of a report sources have described as "explosive" has been delayed until next month.
Former world champion Nicole Cooke has accused the organisation of sexism.
And Howden was criticised for his performance in front of a parliamentary select committee at the end of last year.
"The appointment of an independent chair brings British Cycling more closely in line with the new code for sports governance," Howden said.
Bob Howden has stepped down as chairman of British Cycling, but will remain the organisation's president.