The court, which has heard from around 90 witnesses during two weeks of public hearings, said on Thursday it would announce at noon (1000 GMT) whether the election result was valid or if a new vote would be held.
The FPÖ's Norbert Hofer, 45, topped the poll in the first round of the election back in April, but ultimately lost out to 72-year-old Alexander Van der Bellen, an independent backed by the Greens, by just 30,863 votes in the May 22nd run-off.
Hofer - who would have been the first far-right head of state of an EU country if elected - alleged that there had been numerous procedural irregularities in the vote.
Preliminary results on the evening of the election had given him a narrow lead but after some 700,000 postal votes were counted, Van der Bellen was declared the winner of the largely ceremonial post.
However, the court hearings confirmed that tens of thousands of postal votes were counted in an irregular manner - either because they were counted after the allocated time or by people not authorized to do so.
Van der Bellen's lawyer described the transgressions as having an "insignificant" impact on the ballot.
If the Constitutional Court were to invalidate the election it would send shockwaves through Austria, which would be obliged to return to the polls in the autumn.
Van der Bellen is scheduled to be sworn in on July 8th.
If, however, a new election is ordered, outgoing president Heinz Fischer will be replaced on an interim basis by three parliamentary officials - one of whom is Hofer.