Collier is the first Longhorns player to be the WNBA's top pick and the second from the Big 12, following Baylor center Brittney Griner in 2013.
The Wings took another post player, 6-foot-5 Awak Kuier of Finland, with the No. 2 pick. It's the first time in league history that a team had picks Nos. 1 and 2. The Wings acquired the top pick in a February trade after being awarded the second choice in the draft lottery.
"Needless to say, we are thrilled with the results of the draft for our organization," Wings president and general manager Greg Bibb said. "We took another big step forward tonight with the progress of our team. Obviously with drafting Charli and Awak we got the two best players in the draft."
The 6-foot-5 Collier averaged 19 points and 11.3 rebounds per game while shooting 51.1% from the field for the 21-10 Longhorns, who advanced to the Elite Eight. Collier is a draft-eligible junior because she turns 22 in 2021.
She will be playing for a pro team in her native Texas; she is from Mont Belvieu in the Houston area.
"My heart is racing right now because I worked so hard for this," Collier told ESPN's Holly Rowe. "This is a game that I love, I deserve to be here, and I'm built for it. This is my moment."
Collier is the third true junior to be the No. 1 pick after Notre Dame guards Jewell Loyd in 2015 and Jackie Young in 2019. Tennessee's Candace Parker was a junior in eligibility when she was No. 1 in 2008, but she had been in school four years, having redshirted what would have been her first season in 2004-05.
Kuier, 19, plays professionally for Ragusa in Italy, where she has averaged 8.9 points and 6.8 rebounds per game this season and won a playoff game Thursday before getting drafted. She doesn't turn 20 until August.
Kuier was born in Cairo after her parents fled war-torn South Sudan. When she was 2 years old, her family immigrated to Finland. She becomes the first Finnish player drafted in WNBA history and the seventh international player who did not play U.S. college basketball to have been selected in the top five of the draft.
Dallas went 8-14 and missed the playoffs at ninth place in last year's condensed season in Bradenton, Florida. Like the rest of the WNBA teams, the Wings will be back in their home market this season, playing at College Park Center in Arlington, Texas.
Vickie Johnson is in her first season as Wings coach; she previously was a head coach in San Antonio and played 13 seasons in the WNBA. In Collier and Kuier, Johnson and the Wings get two players with great size as well as scoring and rebounding ability.
"An elite basketball player, so happy that she will be my teammate. Been following her, watching her game," Collier said of Kuier. "Six-foot-5, long, versatile. Can't wait to get to play with her and know her as a basketball player and a teammate."
Dallas also added Arkansas scoring whiz Chelsea Dungee at No. 5 with their third first-round pick. Dungee gives the Wings another offensive-minded guard along with third-year pro Arike Ogunbowale.
McDonald continues incredible 2021, drafted No. 3 by Atlanta Dream
Aari McDonald is selected No. 3 overall in the 2021 WNBA draft by the Atlanta Dream, making her the first player from Arizona to be drafted in the first round.
The Atlanta Dream took NCAA tournament star Aari McDonald at No. 3. The guard led Arizona to the national championship game and becomes the first Wildcats player to be taken in the first round of the WNBA draft.
The first big surprise of the draft came at No. 4, when the Indiana Fever took West Virginia guard Kysre Gondrezick, who was projected by most to be taken in the second or third rounds. She led the Mountaineers (22-7) with 19.5 points per game last season.
New York chose Michaela Onyenwere of UCLA with the sixth pick. Los Angeles took Jasmine Walker of Alabama seventh, Chicago drafted Australian Shyla Heal eighth and Rennia Davis of Tennessee went to Minnesota ninth. Stephanie Watts of North Carolina went 10th to Los Angeles.
The defending champion Seattle Storm took Aaliyah Wilson of Texas A&M next. Wilson didn't stay in Seattle for long, as she was traded to Indiana for Kennedy Burke. WNBA finalist Las Vegas drafted Iliana Rupert from France to close out the first round.
Dallas closed out its four picks in the first 13 by choosing Dana Evans of Louisville, who had been projected to be taken a lot sooner.
"It's a blessing, excited to finally hear my name," an emotional Evans said. "It's motivation, didn't expect to [fall] this far. I'm ready to take on whatever I got to do."
The Washington Mystics became the first team in WNBA history not to make a selection in the draft. The Mystics traded all three of their picks to bring in former league MVP Tina Charles last year.
For the second season in row, the three-round draft was virtual due to the COVID-19 pandemic. WNBA commissioner Cathy Engelbert, who announced the picks from her home last season, was in an ESPN studio in New York while players were at home, appearing virtually when they were drafted.
With potentially as few as 144 roster spots in the WNBA and so many players under contract or still on rookie-scale deals, there are not many spots open for players to make teams. There's a good chance that fewer than a dozen draftees will be on opening-day rosters.
"It's really difficult to find a spot in this league and stick," Los Angeles coach Derek Fisher said. "Coming off 2020, last year with the draft where players that got drafted didn't get an opportunity to go to training camp and earn a spot ... it will be difficult for every player who was drafted tonight to stay with the team."
The Sparks drafted five players Thursday night.
Training camps open around April 25, and the season starts May 14.
The Associated Press contributed to this report.