Strache, who had to resign as party leader and vice-chancellor over the "Ibiza-gate" scandal, has won the 33,000 "preference votes" necessary to leapfrog his party colleagues and gain a seat, according to the APA agency.
The preference votes system means voters can specify their preference for a candidate on a particular party list.
Strache, 49, had been in last place within the FPÖ's list and it is not clear whether he will actually take up the seat.
Strache resigned on May 18th after explosive footage emerged from a hidden-camera sting filmed in a luxury villa on the island of Ibiza, in which he appears to offer public contracts in exchange for campaign help from a fake Russian backer.
Despite calling his own actions "stupid", Strache has since vehemently protested his innocence and painted himself as the victim of a shadowy conspiracy – a message echoed by the FPÖ leadership.
A social media campaign launched by party supporters in the run-up to Sunday's EU parliamentary elections encouraged voters to give Strache a "preference vote" in order to demonstrate he still had support among the party's base.
While the party overall did suffer a drop in its vote to around 17 percent in Sunday's poll, the FPÖ leadership said this was proof they had a solid electoral base and could bounce back in time for early elections expected in the autumn.
On Monday, the FPÖ joined other opposition parties in supporting a no-confidence motion in centre-right Chancellor Sebastian Kurz, meaning a interim government of technocrats is likely to lead the country into the snap elections.