The date was suggested earlier this morning by Interior Minister Wolfgang Sobotka ahead of a government meeting to decide the date for the new election.
The government have now confirmed the election run-off will be held a second time on October 2nd.
"We had today to take a decision on holding the presidential election on October 2. As you can imagine, it was a relatively easy decision to take," Austrian Chancellor Christian Kern told reporters after a cabinet meeting.
The country's constitutional court decided last week that the run-off presidential election originally held in May will have to be held again after finding widespread procedural irregularities.
The court, which questioned more than 60 witnesses in a four day hearing, upheld the challenge brought by the far-right Freedom Party (FPÖ) against its candidate Norbert Hofer's narrow defeat in May's election.
The election was won by independent Green-backed candidate Alexander van der Bellen by a margin of 0.6%.
The FPÖ then launched a legal challenge on June 8 because of "massive irregularities", including allegations that tens of thousands of votes were opened earlier than allowed under election rules and that some votes were counted by people not authorised to do so.
Austria wants OSCE election observers
Both Sobotka and Foreign Minister Sebastian Kurz have said they want the Organisation for Security and Co-operation in Europe (OSCE) to post election observers in the districts where mistakes were made during the first run-off, according to German newspaper Spiegel.
A spokesperson for the OSCE department in charge of monitoring elections - the Office for Democratic Institutions and Human Rights - told The Local Austria, however, that they have not yet received a formal invitation to carry out an assessment.
If the OSCE are invited to carry out an assessment, spokesperson Thomas Rymer said they will take a "number of different factors" into account, including resources and deciding "where they can provide the best value".
"We can then make an assessment on whether to deploy a mission and what format it will take," he said.
He added, however, that as the election re-run is "not a run of the mill" case, he is unsure what the exact process will be.
Countries belonging to the OSCE routinely invite the organisation to assess election environments.
A visit by assessors to Austria in February ahead of the original presidential election in April concluded at that time that it was not necessary to deploy observers to monitor the election.