The Caucasus nation have been without a manager since Berti Vogts' resignation back in October.
Vogts had been in charge of the side for six years, but stepped down shortly after a 6-0 thrashing at the hands of Croatia in a Euro 2016 qualifier.
The Association of Football Federations of Azerbaijan confirmed on Wednesday that Prosinecki is to take over, with his first competitive fixture set to come at home to Malta in their next Group H qualifying game in March.
Having previously turned out for Yugoslavia, Prosinecki starred for Croatia at the World Cup in France in 1998, where they eventually finished third.
He has previously enjoyed managerial stints at Red Star Belgrade - where he won the Serbian Cup in 2012 - and in Turkey with Kayserispor.
