The deal is in place, but can't be official until March. Glazer said the "compensation (is) unclear but I'm told again Chiefs have made a clear commitment to Smith."
Subsequent reports have pegged the compensation as involving a second-round pick and possible two.
The Chiefs have been the favorites for Smith since trade talk began. The Arizona Cardinals were reportedly interested in the quarterback out of Utah, but the 49ers didn't want to trade him to a division rival.
Matt Barrows of the Sacramento Bee reported Wednesday that the compensation for Smith could be a high fourth-round pick in this year's NFL Draft. But Barrows noted that "the question now is whether another team comes forward with a better offer."
Smith broke out in 2011, his sixth season in the league. He led the 49ers to a 13-3 record and a trip to the NFC Championship game. He completed 61 percent of his passes for 3,144 yards and 17 touchdowns.
But in 2012, Smith was injured and never earned his job back. Before he sat in favor of Colin Kaepernick, Smith led the 49ers to a 6-2-1 record. He completed 70.2 percent of his passes for 1,737 yards and 13 touchdowns.