"I tendered my resignation as vice-chancellor of Austria to Chancellor Kurz, and he accepted this decision," an emotional Strache said in a televised statement.
Media reports emerged on Friday alleging that Strache promised public contracts in return for campaign help from a fake Russian backer he met in a luxury villa on the island of Ibiza a few months before 2017's parliamentary elections in Austria.
On Saturday Strache insisted he was the "victim of a targeted political attack" which had used illegal means, but that he was leaving in order to avoid further damage to the government.
Germany's Der Spiegel and Sueddeutsche Zeitung published hidden-camera recordings of the sophisticated sting operation.
In the recordings Strache and his party's group leader in parliament Johann Gudenus are seen discussing with a woman purporting to be the niece of a Russian oligarch how she can invest in Austria.
She says she specifically wants to gain control of the country's largest-circulation tabloid, the Krone Zeitung.
Strache is seen suggesting that new owners could make staff changes at the Krone and use the paper to help his Freedom Party (FPOe) in its election campaign.
He goes on to suggest the woman would then be able to gain access to public contracts.
According the newspapers, Strache says that there would be no resistance among the Krone's editorial staff as "journalists are the biggest whores on the planet".
Both the newspapers that published the footage say they don't have any firm information over who set up the elaborate sting.
Chancellor Sebastian Kurz was due to give his reaction to the scandal on Saturday, with rumours rife that he may push for early elections.
The Krone Zeitung took a particularly outraged tone in its coverage, with its Saturday edition sporting a banner headline reading "The FPOe is done for!".
The Die Presse newspaper's headline talks of a "coalition on the brink".
The Austrian APA agency reports FPOe party sources as saying they want to try to save the coalition with Kurz's centre-right People's Party (OeVP) by replacing Strache as vice-chancellor with Transport Minister Norbert Hofer, also from the FPOe.