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.

The attack took place in the compound of the Helmand MP, Mir Wali. He is believed to have survived but two of his grandchildren are reported to have been killed.
Security forces at the scene say the gunmen are now holding hostages.
Security in Kabul has deteriorated significantly throughout 2016.
The three gunmen began their assault early on Wednesday evening, with at least one of the attackers reported by Tolo News to have detonated explosives inside.
It reported that also among the dead were the 25-year-old son of Kandahar MP Obaidullah Barikzai and two security force members.
A number of people are reported to have been wounded including a former police chief. Gunfire and explosions were recently reported to have been heard at the premises in the west of the city.
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Relatives and friends of Mr Wali - who is reported to have escaped the attackers through the house of a neighbour - are believed to be among the hostages.
The Taliban in a statement said suicide bombers attacked the house because it was hosting an "important gathering of security officials".
The attack again exposes continuing instability in Afghanistan, with regular strikes by suicide bombers and gunmen in recent months in Helmand and in Kabul. The city has been targeted repeatedly by the militants throughout this year.
Police special forces have now been deployed at the scene, officials say, and their priority is to evacuate people from the house and surrounding areas.
The Taliban have made sweeping gains in Helmand - a major opium-producing region - since international coalition forces withdrew from Afghanistan in 2014.
Bob Howden has stepped down as chairman of British Cycling, but will remain the organisation's president.
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Taliban militants in Afghanistan say they are responsible for attacking the house of a member of parliament in Kabul, killing at least five people.