Varoufakis will begin his tour on Monday in Britain, where he taught economics at several universities in the 1980s, for talks with Chancellor of the Exchequer George Osborne.
He then goes to France to meet the ministers of finance and economy, Michel Sapin and Emmanuel Macron respectively. On Tuesday, he will move on to Rome for discussions with Italian Finance Minister Pier Carlo Padoan.
The new Syriza-led government swept to power in elections on Sunday and has already begun unpicking the reforms which were demanded by Greece's European Union partners and the International Monetary Fund in return for a €240 billion EU-IMF package.
The new government says it is scrapping the austerity-minded reforms and wants to erase part of the huge national debt in order to help Greece recover from a painful six-year recession.