The former MP and junior minister said that his position had been "undermined" after the Welsh Conservative Party chose Nick Bourne to take over rather than his deputy, David Davies, 29.
Mr Richards, 52, intended to step down only temporarily after being charged with causing grievous bodily harm to Cassandra Melvin, 22, in Kew, south-west London, last month, allegations he has dismissed as "complete fabrication". He has been bailed to appear in court next month.
Mr Bourne, the party's former finance spokesman, was William Hague's choice for leader of the Welsh party but was narrowly defeated by Mr Richards in a ballot last autumn.
Mr Richards was known as "Redwood's Rottweiler" during his earlier term as a Welsh Office minister in John Major's government and provoked uproar by calling all Welsh Labour councillors "fundamentally corrupt".
He was forced to resign from central government over allegations about his private life in a newspaper. His abrasive style has disrupted the consensus politics of the Assembly since it opened in May and Mr Bourne's supporters felt it was time for a more moderate leadership.
Mr Bourne was elected after a two-hour meeting by senior Welsh Tories, including the nine Assembly members and the Conservative Party's Welsh Affairs spokesman at Westminster, Nigel Evans.
Mr Richards also attended but left early after appealing to members to back Mr Davies. He said in a statement last night: "I asked the Tory group to endorse my appointment of David Davies.
"They did not do so. I therefore feel my authority as leader has been undermined and I have no choice but to resign."
His decision was welcomed in London by the Tory party chairman, Michael Ancram, who praised him for the "dignified and honourable" way in which he stood down.
"I wish him well in his forthcoming fight to clear his name," Mr Ancram said. "I am confident that he will continue to support and contribute to the party in the future and I look forward to him doing so in the Assembly."
However, in his statement, Mr Richards said only that he would continue to work hard "for all of my constituents" in the Assembly.
Conservative Central Office said there would now have to be a new contest to select a permanent successor to Mr Richards. However, many senior Tories were hoping that Mr Bourne would be elected unopposed.
Mr Bourne said afterwards that there would be a senior role for Mr Davies.
Mr Richards' future role is less certain. Mr Bourne said Mr Richards was in an "extremely difficult position" and would need time to consider his next move.
Mr Davies said he would abide by the decision his colleagues had taken.Reuse content