France's President François Hollande also congratulated Tsipras adding that he hoped Greece would continue to support the "growth and stability" of the eurozone.
The French president recalled "the friendship that unites France and Greece and expressed his desire to Mr Tsipras to continue the close cooperation between our two countries, to support the growth and stability of the eurozone, in the spirit of progress, solidarity and responsibility that is at the heart of our shared European values," the statement said.
The Greeks on Sunday handed a clear victory to Syriza, "making history" and "leaving austerity behind" them, said Tsipras, the first European leader elected on a platform of explicitly rejecting the harsh policies imposed by the EU and its members.
Tsipras has vowed a raft of anti-austerity pledges including renegotiating the terms of Greece's €240-billion ($269 billion) bailout with the European Union and the International Monetary Fund, raising the minimum wage and increasing pensions for the poorest.
Reacting to the victory Jean-Luc Melenchon, France's most prominent far-left politician described the victory for the anti-austerity party as "pure happiness".
"This is a new page for Europe. Maybe we can take the opportunity to rebuild Europe, which has become the federal Europe of the liberals,” Mélenchon told BFM TV.
“The Greeks are trying to break out of this straight jacket and thanks to them, maybe we will be able to lay out all the figures on the table, that has made life hellish in Europe.”
Members of France's ruling Socialist party, which last year saw a rebellion by several anti-austerity MPs against Hollande's own austerity policies, also congratulated Syriza.
"The victory of a party on the left is always good news for the Socialist party in France," said Jean-Christophe Cambadélis, the first secretary of the party.
One of those rebels, former education minister Benoit Hamon, said: "The French government clearly now has to support future Greek government in its desire to end austerity and reconnect with economic and social justice, he said.
On the opposite side of France’s political spectrum, the far right were also heralding the victory of the radical-left Greek party, because it represents a blow to the EU.
Jean-Marie Le Pen, the honorary leader of the National Front said the result of the Greek elections reflected a “renunciation” of Europe.
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Although Le Pen’s party does not share the same ideas as Syriza, and the father of Marine believes Tsipras will “come under too much pressure to be able to keep his promises”, he welcomed “the defeat of the European Union in Athens”.
Speaking before Sunday's election Marine Le Pen had angered the French far-left by saying the National Front would welcome Syriza's victory.
"We do not agree with all of their programme, especially on their plans for immigration. But we will celebrate their victory," Le Pen said last week.
"There is a fracturing in Europe, which is seeing the people taking power against the totalitarianism of the European Union and their accomplices, the financial markets," she added.