Recent hacked emails are "consistent with the methods and motivation of Russia-directed efforts", the Department of Homeland Security said.
Data revealing discussions within the Democratic Party was hacked earlier this year.
Some states reported "probing" attempts made on "election-related" systems.
However, officials said those attempts could not be directly linked to the Russian government.
Russian officials told Interfax news agency the claims it was involved in the cyber attacks were "nonsense".
But a joint statement from the Department of Homeland Security and the Director of National Intelligence on Election Security said high-ranking officials at the Kremlin were almost certainly involved in the successful attacks.
"We believe, based on the scope and sensitivity of these efforts, that only Russia's senior-most officials could have authorized these activities," they said.
However, altering any actual ballots or election results would be "extremely difficult", they added, because of a decentralised system and multiple checks and balances.
A number of embarrassing emails have come to light during the 2016 election campaign.
In July, a hacker calling himself Guccifer 2.0 claimed responsibility for the release of documents from the Democratic Party.
Gigabytes of files including emails and other documents that revealed the inner workings of the Democratic National Committee (DNC) were taken.
At an early stage, many US officials linked the breach to Russia. At the time, Moscow denied any involvement and denounced the "poisonous anti-Russian" rhetoric from Washington.
The leaked emails appeared to show that Democratic Party officials were biased against Bernie Sanders in his primary race against Mrs Clinton.
The hack led to the resignation of the party chairwoman Debbie Wasserman Schultz and sparked protests at the national convention in Philadelphia.
Adam Schiff, a senior member of the House of Representatives Intelligence Committee, said he applauded the decision to publicly name Russia as the culprit.
"All of us should be gravely concerned when a foreign power like Russia seeks to undermine our democratic institutions," he said.
He called for co-operation with "our European allies" to develop a response.
US officials have formally accused Russia of cyber attacks against political organisations in order "to interfere with the US election".