The AFC West side gave up their second-round pick in this year's draft in a trade with the San Francisco 49ers for the 28-year-old.
The general manager told the Chiefs' website: "In today's football, truth be told, you need a quarterback to sustain wins.
"After evaluating 20-something players both in college and pro football, I said earlier and I'll say today, Alex Smith was the best option for this organisation. I still stand firm by that.
"The more I'm around him, the more I embrace him as a man, as a leader. Statistically and watching the film his performance on the field speaks for itself. With the coaching staff in place, it will benefit us."
Smith spent eight season with the 49ers, before losing his place to Colin Kaepernick midway through the 2012 season.
The Chiefs will have the first pick in the draft later this week, having finished last year with the worst record in the league.