The 55-year-old Kiwi has agreed to stay at the Scottish club until at least 2020, BBC reported.
Rennie, whose current deal is set to expire at the end of the season, is currently in his second year at the club.
"I'm going to be here for at least another year and a half - possibly longer," Rennie told BBC.
"It's been really good. We're happy, and my wife is happy, that's the key.
"If I'm not here who is going to be running the show and contracting? It gives players clarity over who is going to be here."
Rennie coached the Chiefs to back-to-back Super Rugby titles in 2012 and 2013 but left the team in 2017.
Since replacing Gregor Townsend as head coach at the Warriors, Rennie has led the Warriors to the Pro14 semifinals in his first season.
Rennie's name had been mentioned as a possible successor to Steve Hansen, who announced in December that he would be stepping down as All Blacks mentor after this year's World Cup in Japan.
Hansen has been involved with the All Blacks since 2004 as an assistant coach, after previously coaching Wales, and since 2012 as head coach.
Hansen said in making his intentions clear almost 10 months out from the World Cup, he hoped to give New Zealand Rugby the longest-possible time to find his successor.
"This is a critical process which shouldn't be rushed and shouldn't be made in the turbulent period that tends to follow a Rugby World Cup campaign," Hansen said.
Another early favourite, Ireland's Kiwi coach Joe Schmidt, said in November he would "finish coaching" after the tournament in Japan.
That leaves Ian Foster, Hansen's assistant, New Zealand-born Wales coach Warren Gatland, who coached the British and Irish Lions to a drawn series against the All Blacks in 2017, Montpellier's Vern Cotter, and Crusaders coach Scott Robertson as leading candidates.