The Championship club are seeking a replacement for Derby-bound £5m man Martyn Waghorn.
Defeat to Burnley ensured Aberdeen failed to reach the third qualifying round of the Europa League for the first time in five years.
Windass signed a contract extension as recently as February.
He has managed three appearances for his country Croatia and was shortlisted in the country's 32-man preliminary squad for the World Cup in Russian Federation, but failed to make the final cut.
Barišić becomes the 11 signing of the summer for Rangers, as Steven Gerrard continues to revamp the squad.More news: Tesla’s Big Question: Better or Worse Off as Private Company
The left-back is said to be an attacking, modern day defender who will assist the forward play of the Gers as well as doing his stuff in defensive areas. I'm really excited to play with him again.
"I am very excited to be part of Rangers - it's such a big family and it's the club with the most trophies in the world".
"I will give my heart at Ibrox and every other stadium for Rangers, and I think that this is the most important thing for me".
He started his career at Swansea's bitter rivals Cardiff City and rose through the youth ranks with the Bluebirds.
Meanwhile, Greg Docherty is set to join Shrewsbury Town on a season-long loan deal.