The 52-year old formerly coached Wellington, Manawatu and the New Zealand Under-20s, and says an opportunity to take control of a top European side was too good to refuse.
"The opportunity to work with such an exciting group of players at a club that has such big ambitions and a great winning culture was one I couldn't turn down.
"It is no secret I have been interested in coaching abroad and this chance with Scottish Rugby fitted the bill perfectly.
"As a coach, you want to test yourself in new environments with new challenges. The work Gregor and his team have done at the Warriors speaks for itself and I am very motivated to continue that success and build the club."
Rennie will have one last campaign with the Chiefs next season, with the team looking to announce his long-term replacement in the next few months.
Scottish Rugby Union chief executive Mark Dodson said: "It is a clear indication of the progress Scottish Rugby and Glasgow Warriors are making that we can attract a coach of Dave's experience to Scotland to work with our players.
"Gregor has developed a great winning culture at Glasgow Warriors and I'm very confident Dave will be able to build on that solid foundation to bring more success to the club.
"We have a group of talented Scottish players at Glasgow and we want to maintain their progress and this appointment will expose them to fresh ideas and new approaches to the game. Dave's experience at the Chiefs and at New Zealand age-grade level can only help to develop them and the team further."
Warriors managing director Nathan Bombrys added: "We are incredibly proud at Glasgow Warriors that Gregor will be the next Scotland national coach at the end of next season"
- with AAP
