The charges were drawn up by Special Counsel Robert Mueller, the former FBI director who is looking into alleged Russian interference in the November 2016 vote and whether any members of Trump's campaign team colluded with Moscow, AFP reported.
Democratic leaders immediately called for Trump to cancel Monday's scheduled meeting with the Russian president in Helsinki, but the White House said the summit would go ahead.
The 29-page indictment issued Friday accuses members of the Russian military intelligence agency known as the GRU of carrying out "large-scale cyber operations" to steal Clinton campaign and Democratic Party documents and emails.
"There's no allegation in this indictment that any American citizen committed a crime," Deputy Attorney General Rod Rosenstein said in announcing the charges at a press conference in Washington.
Rosenstein said he briefed Trump about the indictment before Friday's announcement and that the timing was determined by "the facts, the evidence, and the law."
Trump on Saturday responded by blaming the administration of former president Barack Obama for failing to act.
"Why didn't they do something about it, especially when it was reported that President Obama was informed by the FBI in September, before the Election?" he tweeted.
Speaking in Britain before the indictments were unveiled, Trump said he would ask Putin about the allegations of election meddling.
"I will absolutely, firmly ask the question, and hopefully we'll have a good relationship with Russia," he told a press conference with British Prime Minister Theresa May.
The indictment alleges that beginning in March 2016, the GRU agents began targeting over 300 employees and volunteers of the Clinton campaign, the Democratic Congressional Campaign Committee (DCCC) and the DNC.
Around June 2016, they began releasing tens of thousands of the stolen emails and documents using "fictitious online personas, including 'DCLeaks' and 'Guccifer 2.0,'" the indictment said.
Some of the documents and emails were released through a website identified in the indictment only as "Organization 1" – believed to be Julian Assange's WikiLeaks.
Other documents and emails were made public through a website and Twitter account known as DCLeaks, which the GRU falsely attributed to a group of "American hacktivists".
Mueller previously indicted 13 Russians and three companies for allegedly interfering in the presidential vote.
Former Trump campaign chairman Paul Manafort has been charged with money laundering and other crimes, while former national security adviser Michael Flynn has admitted lying to the FBI.
Russia rejected accusations that it interfered in the US presidential election in a bid to help Trump win.
“It is regrettable that spreading false information has become the norm in Washington, and indictments are based on openly political motives,” said the Russian Foreign Ministry in a statement on Friday, adding, “Obviously, the purpose of this is to spoil the atmosphere” ahead of the Putin-Trump summit slated to be held in the Finnish capital of Helsinki on Monday.
The Russian ministry also blamed the “influential political forces of the United States, which oppose the normalization of [US-Russia] relations... and have been manufacturing blatant slander for two years.” It also described the whole case, which it said is supported by “no evidence,” as a “shameful comedy” whose purpose is to “disgrace” the US.