Const. Brian Montague says the van was stolen near the Metrotown shopping centre in Burnaby, B.C., after 11 a.m. on Tuesday.
He says the bus was slowing for a stop when it was hit, and the driver of the van died at the scene.
Montague says five passengers aboard the bus were treated in hospital for minor injuries but the bus driver was not injured.
The fatal collision happened during the lunch hour along a busy transit corridor, which was blocked for several hours as investigators gathered evidence.
Police are not currently releasing any details about the deceased driver.