A report in the New York Times says the agencies had “high confidence” about Russian involvement in hacking.
A CIA assessment reported by the Washington Post made similar findings.
But Mr Trump’s team dismissed the CIA line, saying: “These are the same people that said Saddam Hussein had weapons of mass destruction.”
Russian officials have repeatedly denied the hacking accusations.
On Friday, US President Barack Obama ordered an investigation into a series of cyber-attacks, blamed on Russia, during the US election season.
The hacks targeted emails at the Democratic Party and a key aide to presidential nominee Hillary Clinton.
In October, US government officials pointed the finger at Russia, accusing it of meddling in the campaign.
Now, senior administration officials quoted by the New York Times say they are confident that Russian hackers also infiltrated the Republican National Committee’s computer systems as well as those of the Democratic Party, but did not release information gleaned from the Republican networks.
Intelligence agencies say the Russians passed on the Democrats’ documents to WikiLeaks, the Times reported.
Democrats reacted furiously when email accounts of the Democratic National Committee and Mrs Clinton’s campaign chairman, John Podesta, were hacked.
The Podesta emails were revealed by WikiLeaks and posted online.
Quoting an unnamed “senior US official”, the Washington Post said “intelligence agencies” had “identified individuals with connections to the Russian government who provided WikiLeaks with thousands of hacked emails from the Democratic National Committee and others, including Hillary Clinton’s campaign chairman”.
At one point in the campaign, Mr Trump publicly encouraged Russia to “find” Mrs Clinton’s emails, although he later said he was being sarcastic.
Democrats claimed the hacks were a deliberate attempt to undermine Mrs Clinton’s campaign.
White House spokesman Eric Schultz said President Obama wanted the investigation carried out on his watch “because he takes it very seriously”. “We are committed to ensuring the integrity of our elections,” he added.
It is not clear if the contents of the review will be made public.