The move by Kurz, who denies wrongdoing, satisfied his coalition partner, the Greens, and came just three days before a special session of parliament at which they were preparing to back a motion of no-confidence that would have forced him out.
At the same time, his resignation is more a matter of form than substance in terms of policy. He plans to stay on as his party's leader and become its top lawmaker in parliament, and he is likely to continue to call the shots in the coalition.
"I would therefore like to make way in order to end the stalemate, to prevent chaos and to ensure stability," Kurz said in a statement to the media.
He added that he was proposing Foreign Minister Alexander Schallenberg, a career diplomat backed by Kurz's party, take over as chancellor, whom the Greens soon made clear they accepted.
"I believe this is the right step for future government work," Greens leader and Vice Chancellor Werner Kogler said in a statement, adding he had had a "very constructive" working relationship with Schallenberg and would meet him on Sunday.
A star among Europe's conservatives known for his hard line on immigration, Kurz, 35, became one of the continent's youngest leaders in 2017 when he formed a coalition with the far-right Freedom Party that collapsed in scandal in 2019. Parliament sacked him but he won the snap election that followed.
He has so far been unchallenged as leader of the People's Party (OVP) - he was reappointed in August with 99.4% support.
