Analysts said this new departure might even see Faymann's Social Democrats (SPOe) taking the radical and dangerous gamble of dropping its historic opposition to a tie-up with the far-right.
The SPOe and their centre-right "grand coalition" partners the People's Party (OeVP) have dominated Austrian politics since World War II but their support has been sliding for years.
During the last general election in 2013, they only just scratched together a majority, and polls suggest they will fail to do so again at the next ballot in 2018.
Speaking Monday, Strache said Faymann's resignation "does not solve the SPOe's basic problem, which is its utterly wrong policies (decided) over the heads of people and against Austria's interests."
Tapping into unease over Europe's ongoing migrant crisis, the FPOe is leading opinion polls and on April 24, its candidate won the first round of elections for the largely-ceremonial post of president.
Norbert Hofer, 45, who presents himself as the friendly and reasonable face of the FPOe, will now be up against Alexander van der Bellen, a former head of the Greens who came second, in a May 22 runoff.
This dismal performance, due also to a worsening economic situation and the coalition's inability to agree reforms, means that for the first time since 1945, the president will not be from one of the two centrist parties.
This could result in a situation in which the new president makes use of some of the head of state's considerable but hitherto unused powers, such as firing the government or dissolving parliament.
Deputy Chancellor Reinhold Mitterlehner, head of the OeVP, will replace Faymann on an interim basis but it was unclear who would be his permanent successor as chancellor and SPOe boss.
