The 420-0 House vote, with four conservative Republican lawmakers voting "present", gave Democrats who control the chamber a political victory and put pressure on Attorney General William Barr to make the report public after Mueller submits it to him.
"It is important that Congress stand up for the principle of full transparency at at time when the president has publicly attacked the Russian investigation", said Nadler.
Some Democrats have voiced concern that Barr could withhold evidence of possible misconduct by Trump, under Justice Department policies that oppose bringing criminal charges against a sitting president and discourage releasing explanations when a person has not been charged with a crime.
In February, six House Democratic committee chairs, led by Judiciary Chairman Jerry Nadler of NY, made a similar request in a letter to Barr.
House Democrats already have vowed to subpoena the report and go to court if necessary to win its full release.
"I hope this will be a bipartisan vote to tell the American people, you have the right to and ought to know the results of this report", House Majority Leader Steny Hoyer, D-Md., said on Thursday. He said he has no reason to believe that Barr won't follow the regulations. Those regulations require only that the report explain the decisions to pursue or to decline prosecutions, which could be as simple as a bullet point list or as fulsome as a report running hundreds of pages. "And in the end, I think the department understands they're going to have to make this public".
"I want the American people to know as much as they can and see as much as they can", said Hurd, a former Central Intelligence Agency officer.
White House spokesman Hogan Gidley called the resolution "ridiculous".
"They came in and so many of them said they wanted to work with the president and get things done for infrastructure and health care and instead they're moving on all these radical ideas", Gidley said of Democrats in an interview on Fox News.
Democrats have also made clear they plan to use all the tools at their disposal, including subpoena power, in an effort to make the report available to the public.
Democrats are anxious that Barr's strict defense of his own prerogative, combined with his stated respect for Justice Department rules advising against both the indictment of a sitting president or impugning an unindicted individual in an investigative report, means potential information implicating President Donald Trump in alleged wrongdoing could be buried.
Several Republicans have also agreed that Mueller should release not simply the full report, but any and all investigative materials that informed it.
Republican Sen. Chuck Grassley of Iowa introduced legislation with Democratic Sen.