The Heat traded their first-round pick, No. 26 overall, and two second-round picks to the Charlotte Hornets to move up two spots to grab Napier with the 24th selection.
James praised Napier after he led Connecticut to a second NCAA title in the past four years but he did not consult with the Heat on the selection. However, James' thoughts on Napier were known in the organization, and the Heat spent several days investigating options to trade up to acquire him.
Napier said he hoped his arrival would help persuade James to return to Miami.
"I would hope so," Napier said. "He's one of the best players in the world. So if me going there helps him come back, it just betters our chances of being a complete team."
After the season, James called for the Heat to upgrade "at every position" before next season.
James took to Twitter on Thursday night after Napier was drafted:
My favorite player in the draft! #Napier
- LeBron James (@KingJames) June 27, 2014
"I know LeBron tweeted something out in the NCAA [tournament] about him," Heat president Pat Riley said after the draft. "Why not. If LeBron and I have the same taste in talent, so be it. But he didn't call me on the phone, or he didn't make a point to me about it."
Napier, who can play both guard spots and is an effective shooter, fills the mold of players Riley prefers because he played four years in college. He averaged 18 points and shot 41 percent from 3-point range during his senior season.
"He's a very competitive person, and I think competitive without a huge ego, too," Riley said of Napier. "He's a winner. He's talented and he's skilled. You just have to watch him play the game and you can see the competitive level we all like."
The move could affect the future of Heat starting point guard Mario Chalmers, who will become an unrestricted free agent next week.
Napier said he's eager to prove himself in the NBA.
"No, the chip never leaves my shoulder. It will never leave my shoulder," Napier said. "That's what makes me who I am. And I was saying that not to belittle any other point guards. There's a reason why they're here. But I was just saying that because that's who I am. I wouldn't be Shabazz Napier if I wouldn't have said that. I believe it, and I'm going to prove it.
"What I always learned was that whatever you put in is what you're going to get out. If I don't put in the work, it's not going to show. So there's always a chip on my shoulder to prove to myself that I'm the best, and to do that, I've got to work hard."
The Heat drafted guard P.J. Hairston for Charlotte to complete the swap. Miami also gave the Hornets the No. 55 overall pick (Semaj Christon) in the second round Thursday, a 2019 second-round pick and cash considerations.
Information from ESPN.com's Michael Wallace and Royce Young was used in this report.