The Italian premier phoned Tsipras on Sunday evening, after his election success was announced, government sources told Ansa.
With over 99 percent of the vote counted, Tsipras' left-wing Syriza party won 35.46 percent in the weekend election. The results put him well ahead of the conservative New Democracy party, with 28.09 percent.
Greeks were however notably tired when faced with the country's fifth election in six years, with over 43 percent of eligible voters deciding not to take part.
The snap election was called last month after Tsipras lost his parliamentary majority.
In winning the election he now has greater backing for a tough reform agenda, which is intended to help Greece recover from its economic downturn.