Mr Assange said Russia was not the source for the site's mass leak of emails from the Democratic Party.
Mr Trump has now backed that view in a tweet. He wrote: "Assange... said Russians did not give him the info!"
The president-elect has repeatedly refused to accept the conclusions of the US intelligence community.
Several US agencies including the FBI and the CIA believe Russia directed hacks against the Democratic Party and the campaign of its presidential candidate Hillary Clinton.
The information, released through Wikileaks and other outlets, was intended to help Mr Trump win the election, say the FBI and CIA.
On Tuesday evening, Mr Trump said an intelligence briefing he was due to receive on the issue had been delayed.
"Perhaps more time needed to build a case. Very strange!" he wrote.
But US intelligence officials insisted there had been no delay in the briefing schedule.
In an interview with Fox News, Mr Assange repeated his claim that Russia was not behind the leak.
He also said a 14-year-old boy could have carried out one of the hacks, on the email account of John Podesta, a top aide of Mrs Clinton.
In 2010, several leading Republican figures were calling for the Wikileaks founder to be imprisoned after his website published thousands of embarrassing diplomatic cables leaked by former Army Pvt Chelsea Manning.
Mr Trump tweeted twice on Wednesday morning in support of what Mr Assange said on Fox News.
In another development, Mr Trump's pick for secretary of state, Rex Tillerson, has agreed he will cut all ties with Exxon Mobil and comply with conflict-of-interest requirements.
Meanwhile, Republicans have ditched a plan to gut the independent body that investigates political misconduct after a backlash.
The lawmakers' surprise vote to strip the Office of Congressional Ethics of its independence prompted public uproar and a dressing down from Mr Trump on Twitter.
The secretive move, which overshadowed the first day of the 115th Congress, was reversed in an emergency meeting.
The ethics body was set up in 2008 following a slew of scandals that resulted in several House lawmakers being jailed.
Mr Trump made cleaning up corruption in Washington a key theme of his campaign.
Republican Speaker of the House Paul Ryan had argued unsuccessfully against the rule change, which was adopted on Monday night in a closed-door meeting.
As the news spread, internet searches for "who is my representative" rocketed, according to Google Trends, and constituents tried to call and email lawmakers to express their disgust.
House Republicans called an emergency meeting and abruptly voted to undo the change.
Mr Ryan - who was re-elected by fellow lawmakers on Tuesday as House Speaker - had urged his party to seek bipartisan support and to wait to push for the change later.
Author: US & Canada