Benkovic, whose arrival at the King Power Stadium is thought to be the first part of a double signing alongside Freiburg defender Caglar Soyuncu worth a combined £33.5m, has put pen to paper on a five-year contract that will keep him with the Foxes until 2023.
"I will give all my heart to this club, to all the fans, to everybody," the player told LCFC TV.
"Hopefully we'll have a very good result this season. The ambitions of Leicester City are so big. I like the club very much and I think it's a very good step for me to the next level. I'm very happy to be here," he added.
Leicester manager Claude Puel commented, "Filip is an exciting young player who has the potential to develop even more at Leicester City Football Club.
"He has made a big contribution to Dinamo Zagreb over the last three years and has also benefitted from experiencing European football. I know he will give us some great options and competition in the squad and I'm delighted to have him here."
Whether the signing of Benkovic and the possible further arrival of Soyuncu will mean that Harry Maguire is allowed to join Manchester United remains to be seen.