After that, Fusion GPS hired dossier author Christopher Steele, a former British intelligence officer with ties to the FBI and the U.S. intelligence community, according to those people, who spoke on the condition of anonymity.
Elias and his law firm, Perkins Coie, retained the company in April 2016 on behalf of the Clinton campaign and the DNC. Before that agreement, Fusion GPS's research into Trump was funded by an unknown Republican client during the GOP primary.
The Clinton campaign and the DNC, through the law firm, continued to fund Fusion GPS's research through the end of October 2016, days before Election Day.
Fusion GPS gave Steele's reports and other research documents to Elias, the people familiar with the matter said. It is unclear how or how much of that information was shared with the campaign and the DNC and who in those organizations was aware of the roles of Fusion GPS and Steele. One person close to the matter said the campaign and the DNC were not informed by the law firm of Fusion GPS's role.
The dossier has become a lightning rod amid the intensifying investigations into the Trump campaign's possible connections to Russia. Some congressional Republican leaders have spent months trying to discredit Fusion GPS and Steele and tried to determine the identity of the Democrat or organization that paid for the dossier.
Trump tweeted as recently as Saturday that the Justice Department and FBI should "immediately release who paid for it."
Elias and Fusion GPS declined to comment on the arrangement.
A DNC spokeswoman said "[Chairman] Tom Perez and the new leadership of the DNC were not involved in any decision-making regarding Fusion GPS, nor were they aware that Perkins Coie was working with the organization. But let's be clear, there is a serious federal investigation into the Trump campaign's ties to Russia, and the American public deserves to know what happened."
Brian Fallon, a former spokesman for the Clinton campaign, said he wasn't aware of the hiring during the campaign.
"The first I learned of Christopher Steele or saw any dossier was after the election," Fallon said. "But if I had gotten handed it last fall, I would have had no problem passing it along and urging reporters to look into it. Opposition research happens on every campaign, and here you had probably the most shadowy guy ever running for president, and the FBI certainly has seen fit to look into it. I probably would have volunteered to go to Europe myself to try and verify if it would have helped get more of this out there before the election."
Some of the details are included in a Tuesday letter sent by Perkins Coie to a lawyer representing Fusion GPS, telling the research firm that it was released from a client-confidentiality obligation. The letter was prompted by a legal fight over a subpoena for Fusion GPS's bank records.
People involved in the matter said that they would not disclose the dollar amounts paid to Fusion GPS but that the campaign and the DNC shared the cost.
Steele previously worked in Russia for British intelligence. The dossier is a compilation of reports he prepared for Fusion GPS. The dossier alleged that the Russian government collected compromising information about Trump and that the Kremlin was engaged in an effort to assist his campaign for president.
U.S. intelligence agencies later released a public assessment asserting that Russia intervened in the 2016 election to aid Trump. The FBI has been investigating whether Trump associates helped the Russians in that effort.
Trump has adamantly denied the allegations in the dossier and has dismissed the FBI probe as a witch hunt.
Officials have said that the FBI has confirmed some of the information in the dossier. Other details, including the most sensational accusations, have not been verified and may never be.
Fusion GPS's work researching Trump began during the Republican presidential primaries, when the GOP donor paid for the firm to investigate the real estate magnate's background.
Fusion GPS did not start off looking at Trump's Russia ties but quickly realized that those relationships were extensive, according to the people familiar with the matter.
When the Republican donor stopped paying for the research, Elias, acting on behalf of the Clinton campaign and the DNC, agreed to pay for the work to continue. The Democrats paid for research, including by Fusion GPS, because of concerns that little was known about Trump and his business interests, according to the people familiar with the matter.
Those people said that it is standard practice for political campaigns to use law firms to hire outside researchers to ensure their work is protected by attorney-client and work-product privileges.
The Clinton campaign paid Perkins Coie $5.6 million in legal fees from June 2015 to December 2016, according to campaign finance records, and the DNC paid the firm $3.6 million in "legal and compliance consulting'' since November 2015 — though it's impossible to tell from the filings how much of that work was for other legal matters and how much of it related to Fusion GPS.
At no point, the people said, did the Clinton campaign or the DNC direct Steele's activities. They described him as a Fusion GPS subcontractor.
Some of Steele's allegations began circulating in Washington in the summer of 2016 as the FBI launched its counterintelligence investigation into possible connections between Trump associates and the Kremlin. Around that time, Steele shared some of his findings with the FBI.
After the election, the FBI agreed to pay Steele to continue gathering intelligence about Trump and Russia, but the bureau pulled out of the arrangement after Steele was publicly identified in news reports.
The dossier was published by BuzzFeed News in January. Fusion GPS has said in court filings that it did not give BuzzFeed the documents.
Current and former U.S. intelligence officials said that Steele was respected by the FBI and the State Department for earlier work he performed on a global corruption probe.
In early January, then-FBI Director James B. Comey presented a two-page summary of Steele's dossier to President Barack Obama and President-elect Trump. In May, Trump fired Comey, which led to the appointment of Robert S. Mueller III as special counsel investigating the Trump-Russia matter.
Congressional Republicans have tried to force Fusion GPS to identify the Democrat or group behind Steele's work, but the firm has said that it will not do so, citing confidentiality agreements with its clients.
Last week, Fusion GPS executives invoked their constitutional right not to answer questions from the House Intelligence Committee. The firm's founder, Glenn Simpson, had previously given a 10-hour interview to the Senate Judiciary Committee.
Over objections from Democrats, the Republican leader of the House Intelligence Committee, Rep. Devin Nunes (Calif.), subpoenaed Fusion GPS's bank records to try to identify the mystery client.
Fusion GPS has been fighting the release of its bank records. A judge on Tuesday extended a deadline for Fusion GPS's bank to respond to the subpoena until Friday while the company attempts to negotiate a resolution with Nunes.
Julie Tate contributed to this report.