The Chiefs acquired the 10th pick from the Buffalo Bills in return for the 27th pick, their first-round choice in 2018 and a third-rounder (91st overall) this year.
Mahomes is the first quarterback drafted by the Chiefs in the opening round since 1983 (Todd Blackledge).
"Right now Patrick is not absolutely ready to play," Kansas City coach Andy Reid said. "He's got some work to do. We have to be patient with him. He's definitely not a finished product right now.
"But he has tremendous upside. We think he'll fit into this offense very well. He's a good person. He's intelligent. He's got great skill. I just think he'll be a great Kansas City Chief when it's all said and done."
The Chiefs can afford to give Mahomes time to develop. Starter Alex Smith, who turns 33 next month, has two seasons remaining on his contract.
But the Chiefs could release or trade Smith before the 2018 season with minimal financial penalty. He would cost the Chiefs $3.6 million against their salary cap if they moved him before next season.
The Chiefs have not had much luck with QBs in the draft.
The last one they selected in any round to eventually win a game for the team was Blackledge. The Chiefs have taken 22 QBs in the common draft era, and the only one to make it to a Pro Bowl was Mike Livingston (drafted in 1968; Pro Bowler in 1969).
Mahomes will try to right that ship.
While Texas Tech failed to reach a bowl game this past season, the QB racked up gaudy stats, leading FBS with 5,052 passing yards. He joined current Titans QB Marcus Mariota (2014 Oregon) as the only players from a major conference in FBS history to throw 40 touchdown passes and rush for 10 touchdowns in the same season.
Mahomes had the most completions from outside the pocket (55) and under duress (59) among Power 5 QBs last season. He completed 46.2 percent of his passes thrown at least 10 yards downfield in 2016 and his 313 scramble yards ranked second in the Big 12.