"I want to win," Wiggins said shortly after he became the top pick in the NBA Draft on Thursday night at the Barclays Center in Brooklyn. "If (James) wants to win, we'd be good together."
After Duke small forward Jabari Parker went second to the Milwaukee Bucks, the Philadelphia 76ers selected Wiggins' college teammate at Kansas, center Joel Embiid, with the third pick.
The Cavaliers took Wiggins on the 11th anniversary of selecting James, the Ohio native who led the Cavs to 314 regular-season wins and one NBA Finals appearance in six years before famously departing for Miami as a free agent in the summer of 2010.
James opted out of his contract with the Heat earlier this week, which instantly generated buzz about a potential return to Cleveland.
That remains to be seen, but the Cavaliers hope Wiggins will help complete an extended rebuilding project. Cleveland is just 97-215 and has picked first in the draft three times in four years without James.
Wiggins, who averaged 17.1 points per game in his lone season at Kansas, told ESPN, "(I plan on) going in and creating an impact off the bat. Play my game, have confidence in myself. Because I've got to believe in myself before anyone else can."
The Cavaliers had mixed results with their last two No. 1 picks.
While the top 2011 draftee, guard Kylie Irving, has averaged 20.7 points and 5.8 assists in three seasons, the 2013 No. 1 selection, forward Anthony Bennett, missed 30 games as a rookie because of numerous health ailments and averaged just 4.2 points and 12.8 minutes per game, the fewest points and minutes by a No. 1 draft pick in his first season.
Wiggins led off a draft that was turned upside down by the foot injury Embiid sustained recently. With the 7-footer out of the running as the top overall pick, the suspense over whether the Cavaliers would hang onto the No. 1 pick or trade down went to the wire -- and beyond. A few minutes went by between Cleveland's clock expiring and NBA commissioner Adam Silver stepping to the podium.
"I was nervous," Wiggins said on ESPN. "It hit :00 and I felt like another two minutes of waiting. It's crazy."
The Cavs also considered Parker before going with Wiggins. The Bucks quickly snapped up Parker, a physical player who hopes to make an impact from the start.
"They're a young team," Parker said of the Bucks. "I feel like I can contribute right off the bat. I feel like I'm going to be able to grow with that organization, and I'm trying to be a throwback player, only stick with one team."
Embiid didn't have to wait long to learn his destination, as he went to Philadelphia with the third overall pick.
Embiid averaged 11.2 points and 8.6 rebounds per game as a freshman at Kansas. However, the raw Cameroon native, who didn't play organized basketball until he was 16, dropped in the draft after enduring two serious injuries in the last four months.
Embiid missed the final six games of Kansas' season with a stress fracture in his lower back. He hurt his foot within the last two weeks and underwent surgery June 20.
"I wish I could be there," Embiid said during an interview with ESPN from his home in California. "I'm excited the Sixers took me. I still can't believe it."
The Orlando Magic selected Arizona power forward Aaron Gordon with the fourth pick. Rounding out the top 10 were picks by the Utah Jazz (Australian shooting guard Dante Exum), the Boston Celtics (Oklahoma State point guard Marcus Smart), the Los Angeles Lakers (Kentucky power forward Julius Randle), the Sacramento Kings (Michigan shooting guard Nik Stauskas), the Charlotte Hornets (Indiana power forward Noah Vonleh) and the 76ers (Louisiana-Lafayette point guard Elfrid Payton).
The lone senior selected in the lottery was Creighton power forward Doug McDermott, who was picked 11th by Denver and promptly traded to Chicago, along with Nuggets power forward Anthony Randolph, for the Bulls' two first-round picks -- Bosnian center Jusuf Nurkic and Michigan State shooting guard Gary Harris -- as well as a 2015 second-round pick.
Orlando picked Croatian power forward Dario Saric at No. 12 and traded him to the 76ers, along with a 2015 second-round pick and a future first-round pick, for Payton.
Minnesota picked UCLA point guard Zach LaVine at No. 13 before Phoenix ended the lottery portion of the draft by selecting North Carolina State small forward T.J. Warren. Atlanta then grabbed Michigan State power forward Adreian Payne with the 15th pick.
The biggest name selected in the second half of the first round was UConn point guard Shabazz Napier, who led the Huskies to two national championships in four seasons.
Napier fell to Charlotte at No. 24 and was promptly traded to Miami in exchange for the rights to Heat first-rounder P.J. Hairston, Miami's second-round pick (55th overall) and a future second-round pick.
Like Wiggins, Napier might become part of an attempt to woo James during the free agency period. On April 8 -- the day after UConn beat Kentucky in the national championship game -- James tweeted that Napier should be the first point guard selected in the draft. After the trade was announced Thursday, James tweeted that Napier was "My favorite player in the draft!"
Other notables selected late in the first round included Syracuse point guard Tyler Ennis, the clutch shooter who went to Phoenix at No. 18, and UCLA small forward Kyle Anderson, whom reigning NBA champion San Antonio took with the 30th and final pick.
In a trade consummated earlier in the day, New Orleans sent center Omer Asik and $1.5 million to Houston in exchange for a protected 2015 first-round pick.
NOTES: Cleveland picked first for a league-high sixth time. ... The Cavaliers had just a 1.7 percent chance of winning the draft lottery after finishing with the ninth-worst record (33-49) last season. ... Andrew Wiggins, a Canadian native, became the sixth foreign-born player to be picked first overall after Hakeem Olajuwon (1984), Patrick Ewing (1985), Andrew Bogut (2005), Andrew Bargnani (2006) and Wiggins' new teammate and fellow Canadian, Anthony Bennett (2013). ... Baylor C Isaiah Austin, who was expected to be drafted before he was diagnosed last week with Marfan syndrome, was at the Barclays Center and took the stage with commissioner Adam Silver between the 15th and 16th picks. Silver said Austin was "selected by the NBA" as Austin wiped tears from his eyes.