A prominent critic of the EU and its leadership, leftwing economist Varoufakis nonetheless backed a Remain vote during last summer's referendum.
In London to promote his new memoirs today, he said the UK should mimic Norway's European Economic Area membership for up to six years to secure a smooth changeover to a new relationship with Europe.
“After the Brexit referendum on 23 June I was warning that if they [the UK] make the mistake of trying to negotiate a free trade agreement within the two year period after triggering Article 50 they would end up with a lot of egg on their face,” Varoufakis told City A.M.
“The only way of reaching a mutually advantageous set of circumstances in the medium term between the UK and the EU would be to file for a Norway-style agreement for five or six years for a period of transition that is very smooth.
“If you ask for that kind of agreement, [German chancellor Angela] Merkel and [European Commission president Jean Claude] Juncker and [EU chief negotiator Michel] Barnier cannot deny it, they have to to give it to you.
"And that way you allow them to throw this hot potato in the lap of the next Chancellor in Germany, and the next commissioner in Brussels.”
It comes after Theresa May yesterday claimed that Brussels was seeking to interfere in the UK's election.
May's warning has drawn a sharp response from European Council president Donald Tusk, who has warned against talks becoming “emotional”.
“Brexit talks difficult enough. If emotions get out of hand, they'll become impossible. Discretion, moderation & mutual respect needed,” Tusk tweeted today.
#Brexit talks difficult enough. If emotions get out of hand, they'll become impossible. Discretion, moderation & mutual respect needed.— Donald Tusk (@eucopresident) May 4, 2017
At stake are the daily lives and interests of millions of people on both sides of the Channel. #Brexit— Donald Tusk (@eucopresident) May 4, 2017