Clarkson is a 6-foot-5, 22-year-old junior who averaged 17.5 points last season through 35 appearances with the Tigers.
General Manager Mitch Kupchak called Clarkson a "ball-handling guard" that the Lakers expected to be "gone [in the] mid-first round."
"It's a blessing," said Clarkson to reporters in a conference call. "I feel like I'm in a good situation. It was a long draft process. I worked real hard. I feel like I'm in the right situation, I just have to make the best out of my opportunity."
Clarkson shot 50% from the field with the Tigers but he didn't show reliable three-point range -- hitting just 28.1% from behind the arc. Clarkson's 3.4 assists per game also came with 2.7 turnovers.
"I see myself as a point guard, but I can also play the two because of my versatility on defense and my ability to score the ball," said Clarkson.
He'll join the Lakers in July on their summer league squad in Las Vegas.
"[Clarkson is] a good athlete, really good size, good defender, excels at probably attacking the rim," said Kupchak. "[He's] maybe not as good a shooter as he will be when he works on it."
The Lakers also added Kentucky forward Julius Randle with the seventh overall pick earlier in the draft.
"We got two players, so now we're up to six," joked Kupchak. "You've got to get to 13, so it's nice to almost be halfway through."
The Lakers didn't have their own second-round pick (36th overall), which was originally traded to the Phoenix Suns as part of the Nash trade. The Suns moved the pick on to the Milwaukee Bucks, who selected Johnny O'Bryant of Louisiana State.
Before transferring to Missouri, Clarkson played two seasons at Tulsa.