The 28-year-old will officially link up with Villa from Belgian side Gent when the transfer window opens on January 1 and will sign a deal until 2023.
"We are delighted to be signing someone of Lovre's experience and quality," Villa boss Dean Smith said on the club's website.
"He is an outstanding goalkeeper and we are looking forward to welcoming him when he joins at the beginning of January."
Kalinic was a member of the Croatia squad that reached the World Cup final in Russia.
Summer signing Orjan Nyland has been first choice this season but has not convinced for Villa, who are chasing a play-off place and host leaders Leeds United on Sunday.