Previously Cane has been a co-captain in the side, sharing the duties since 2016 with Charlie Ngatai, Aaron Cruden and Brodie Retallick respectively.
But Gatland said in making the announcement: "Sam has co-captained the Chiefs since 2016. He is an experienced campaigner who is well respected by the players and management.
"We believe it was important to identify one person this season to lead the team and that individual would be supported by the team's leadership group."
Having made his debut for the side in 2012, the same year it won its first Super Rugby title, Cane has appeared in 111 games for the side and shared two competition titles after they backed up with a successful defence in 2013.
He suffered a potentially career-ending setback when breaking his neck in South Africa in 2018 but after surgery and rehabilitation he regained his place in the All Blacks last year to play in the Rugby World Cup and earn his 68th Test cap.
Cane has been involved at leadership group level with the All Blacks and his work ethic and rugby knowledge would be an asset for the Chiefs.
Cane said he was looking forward to working with former Wales coach Warren Gatland.
"We are privileged to be able to have a coach of his calibre lead a great coaching group. I am looking forward to work with, and learning off, Warren this season.
"It is an honour to be asked to captain this side and I am excited for the season to kick off," he said.
The Chiefs play the Blues in a warm-up game in Waihi on Friday and then they meet again in their opening game of the Super Rugby season in Auckland on January 31.
"We have a talented squad, with a good mix of experienced and gifted young players. This combined with a fantastic group of experienced leaders, we believe will be the right ingredients to help drive us to another title," he said.