The Labour Party and others sent a letter to Mr Bercow after Theresa May's government said it would not publish the full legal advice on the warnings it may have received regarding the withdrawal.
"By treating Parliament with contempt, the Government has proved it has lost its majority and the respect of the House".
Labour's shadow Brexit secretary Sir Keir Starmer said that the finding of contempt was "a badge of shame" for the Government, with "huge constitutional and political significance".
The vote marked the first time in history a United Kingdom government has been found in contempt of parliament.
"This is the deal that delivers for the British people."
There is no requirement for the government to share legal advice on new policies, nor is there precedent for legal advice to be routinely published.
"The British people want us to get on with a deal that honours the referendum and allows us to come together again as a country, whichever way we voted", excerpts of a speech devised for Parliament read.
Image Labour and the Conservatives accused each other of 'running scared' in relation to a proposed debate
It's an embarrassing defeat for Theresa May's government, who now face five days of Brexit debate, before the crunch vote on the deal agreed with the European Union on December 11.
Ms Haddon said the contempt motion was a "show of force" which could foreshadow both the final vote on the deal and the various amendments lawmakers are trying to attach to it.
In reality, the vote was about putting pressure on a weakened Government.
The government had attempted to have the issue referred to the cross-party Privileges Committee in a prior vote but the proposal was defeated by four votes.
Mr Cox was repeatedly challenged about the issue in the Commons on Monday but insisted it was in the public interest for the advice he gave to ministers to remain confidential.
Attorney General Geoffrey Cox earlier published an overview of his legal advice on Theresa May's Brexit deal and answered MPs questions on it.
Tory MP Anne Marie Morris Newton Abbot earlier intervened on Mrs May to suggest her deal would mean the United Kingdom would be "stuck with the same rule base that we have in the EU".
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