30-year-old Weber debuted for the Chiefs in 2014 and established himself as the franchise's first choice halfback.
He was been stand-in captain for the Chiefs on several occasions during both the 2019 and 2020 Super Rugby seasons.
Cane first captained the Chiefs in 2016.
Since awarded the captaincy, Cane has captained alongside Aaron Cruden, Charlie Ngatai and Brodie Retallick.
Weber is honoured to undertake the role as a captain alongside Cane.