The call which was initiated by premier Stubb discussed about the economic situation in Greece as well as the new government's economic policy.
"I wanted to immediately congratulate Tsipras and open dialogue with the new Greek government," said Stubb.
According to Stubb, it is important for Finland that the Greek government continues the necessary structural reforms and honour the agreements.
The two prime ministers are expected to discuss in more detail during an extraordinary European Council gathering slated for 12 February.
Anti-bailout Radical Left SYRIZA party leader Alexis Tsipras was sworn in on Monday as Greece's new Prime Minister to head a coalition government after winning Sunday's national elections.