Two-time Olympic judo champion Peter Seisenbacher was arrested in Kyiv on sexual assault charges on August 1 after seven months on the run.
A criminal court in Austria requested Seisenbacher's extradition shortly after his arrest by Ukrainian police.
Seisenbacher, 57, failed to show up for the start of his trial on December 19 for the alleged sexual assault of two young girls he coached in the early 2000s, and his whereabouts were unknown for months.
Prosecutors say the alleged abuse took place in Vienna between 1999 and 2004. The women filed charges against their former coach in 2013. If found guilty, he could face a prison term of up to 10 years.
In 1988 in Seoul, South Korea, Seisenbacher became the first judoka to win gold at two consecutive Olympics after also winning in 1984 in Los Angeles.
As a coach, he led the Azerbaijan team to two silver medals at the Rio de Janeiro Games last year.
Previously, he was head coach of Georgia when Lasha Shavdatuashvili won gold in the men's 66-kilogram division at the 2012 London Olympics.