"Man, LeBron, let's do it," Sexton said during ESPN's telecast of the draft, which was held at the Barclays Center in New York.
"Let's do it," Sexton continued. "I seen you needed a few pieces, one or two pieces this past season, and let's do it. Let's go back to the Finals."
Sexton, 19, averaged 19.2 points and 3.6 assists in his only season for the Crimson Tide. He worked out for the Cavs the day after they lost Game 4 of the Finals, and owner Dan Gilbert called him a "very intriguing draft prospect" on Twitter.
Sexton said he was at Game 4, which turned out to be the Warriors' title-clinching win.
"I'm very excited," Sexton said. "I'm glad the Cavs picked me at No. 8. When I was working out for them, I felt like that was one of my better workouts, probably one of my best workouts, actually."
So Gilbert got his man. James' camp also liked Sexton, preferring him to any point guard in the draft, though Cleveland's selection of him does not guarantee James will return to the Cavs.
James can be a free agent in July. Sexton said it would mean "a whole lot" to play with James "because he's one of the best players to ever play basketball.
"Just being able to come in and learn from him, it'll be big for me and big for my growth."
The Cavs had a chance to draft Missouri's Michael Porter Jr., who was often linked with Cleveland. People inside and outside the organization thought earlier this week that Porter would be the Cavs' pick if he were still there at No. 8, but Porter began to plummet on draft boards Wednesday and Thursday over new medical information related to his injured back that needed surgery and forced him to miss all but three games this season.
Porter fell to the bottom of the lottery -- going 14th to the Denver Nuggets.
Sexton, meanwhile, set the school's season and single-game scoring records for freshmen, with 632 points overall and a 40-pointer against Minnesota in November. He shot .336 from 3-point range.
From Mableton, Ga., Sexton is listed at 6-3 and 190. He's known not only as a scorer, but as a fast, high energy player and physical, capable defender. He said "the most important side is the defensive side, just because of all the players you have to go against night in, night out."
The Cavs were ranked 29th in defense last season.
Opposing college coaches say he came "out of nowhere" to star as a freshman, and was in fact named the SEC's freshman and newcomer of the year.
Then again, Sexton was a Naismith High School second-team All-American in 2017.
"It just shows all my hard work paid off," Sexton said. "I just grinded -- started from the bottom and came back up to the top. That was the biggest thing, just show people what I can do."
The Cavs picked eighth thanks to their trade last summer of Kyrie Irving, the point guard they hope Sexton can replace. General manager Koby Altman traded Irving to Boston for three players and two draft picks, including Brooklyn's first rounder this year. Hey, Sexton even wore No. 2 at Alabama -- Irving's number in his six seasons with Cleveland after the Cavs made him the No. 1 overall pick in 2011.
Sexton is Altman's first draft choice as general manager, and the Cavs' first pick in the first round since late in the 2015 draft, when they took Tyus Jones and traded him to Minnesota.
"Of all the guys I've coached in the (NBA), played against in the league, he was arguably the fastest guy I've seen with and without the basketball," said Sexton's college coach, Alabama's Avery Johnson. "But he's got a lot of room to grow. He's going to get better."
The Cavs also have point guards George Hill and Jordan Clarkson on the roster, though they view Clarkson as more of a shooting guard.
Cleveland entered the draft with no second-round pick.
As expected, the Suns drafted Arizona center Deandre Ayton No. 1 overall. The Kings followed with Marvin Bagley III of Duke. The Mavericks moved up from No. 5 to third in a trade with the Hawks to take 19-year-old Euroleague star Luka Doncic of Real Madrid.
Atlanta picked Trae Young from Oklahoma fifth. Jaren Jackson Jr. of Michigan State went fourth to the Grizzlies. The Magic selected Mo Bamba, center from Texas, sixth, and the Bulls drafted Duke center Wendell Carter Jr.