"The election ended a long time ago in one of the biggest Electoral College victories in history." the Trump transition team's statement read. "It's now time to move on and 'Make America Great Again.'"
According to the report, intelligence officials identified individuals with connections to the Russian government who provided WikiLeaks with hacked emails and other documents that were damaging to the Democratic Party and its presidential nominee, Hillary Clinton.
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In October, US intelligence officials formally accused Russia of hacking the Democratic Party after a series of cyberattacks against the organization.
While the US initially thought Russia was trying to sew doubt in the US electoral process, intelligence officials now say Russia's apparent goal was to elect Trump.
The Post's report came hours after President Barack Obama ordered a "full review" of Russia's alleged involvement, due before Trump's inauguration on January 20.
Trump has repeatedly dismissed the possibility of Russia's involvement in the election.
In an interview with Time published this week, Trump said the previous hacks could have been caused by Russia, or China, or "some guy in his home in New Jersey."