"We wanted to send a signal of renewal," said FPÖ leader Heinz-Christian Strache at a news conference on Tuesday.
Krauss succeeds Helmut Günther, who will move to Vienna's parliament to replace current EU representative, Barbara Kappel.
For Strache, Krauss's appointment is a sign that the FPÖ wants to "air out" the city council and "really represent the interests of students".
Krauss, who will give his inaugural press conference next week, is "the youngest district chairman of the FPÖ in Vienna" in Josefstadt, and was also a candidate in the last general election.
The right-wing FPÖ increased its vote significantly in the recent European elections, particularly among the under 29s.
Compared with 2009, the party increased its share of the vote by seven percent, winning a total of 19.7 percent.