"It's indescribable right now," slender power forward Davis, 19, said after shaking NBA Commissioner David Stern's hand. "A great feeling, great experience. I've wanted this all my life, so it's finally here."
Davis's dream night was topped off when his college team-mate Michael Kidd-Gilchrist became the second player taken in the draft when the Charlotte Bobcats made their selection.
Davis and small forward Kidd-Gilchrist, who teamed up to win the US college basketball championship, became the first players from the same school to go one-two in an NBA draft.
"It's crazy," Davis said. "Michael is a great player."
Before the draft, Davis and Kidd-Gilchrist sat with Kentucky coach John Calipari, but they did not talk about going one-two.
"I was shocked at first," Kidd-Gilchrist said about hearing his name called. "I was shocked."
Kidd-Gilchrist's selection at number two was a bit of a surprise, but the choice of Davis was a no-brainer.
"To be drafted number one overall means a lot to me, for a 19-year-old freshman, now professional," Davis said. "The city of New Orleans was great, I had a great time when I went to visit. I just can't wait to get down there and start to play."
The 6-foot-10 (2.08 m) Davis averaged 14.2 points a game for Kentucky and shined on the defensive end, pulling down 10.4 rebounds and nearly five blocked shots a game, and was named Most Outstanding Player of the Final Four.
Davis said he would have to build up his strength when asked about his greatest challenge entering the NBA.
"The physicality. Guys are a lot stronger in the NBA and I know that's one of my weaknesses. So I try to make it a strength, stay in the weight room, try to get tougher."
The Washington Wizards took guard Bradley Beal of the University of Florida with the third pick before the Cleveland Cavaliers tabbed guard Dion Waiters of Syracuse with the next.
Power forward Thomas Robinson of Kansas went to the Sacramento Kings with the fifth pick of the first round.
New Orleans used the 10th pick to take Duke guard Austin Rivers, son of Boston Celtics coach Doc Rivers.
The Houston Rockets had three first-round picks, having added draft choices through trades.
Houston took guard Jeremy Lamb from Connecticut with the 12th pick, added small forward Royce White of Iowa State at number 16 and nabbed forward Terrence Jones of Kentucky at 18.
The first international player taken in the draft was France's Evan Fournier. The shooting guard from Poiters Basket 86 was taken with the 20th pick of the first round by the Denver Nuggets.
First round Draft picks (pick number, NBA team, player, position, origin):
1 New Orleans Hornets - Anthony Davis, Forward, Kentucky
2 Charlotte Bobcats - Michael Kidd-Gilchrist, F, Kentucky
3 Washington Wizards - Bradley Beal, Guard, Florida
4 Cleveland Cavaliers - Dion Waiters, G, Syracuse
5 Sacramento Kings - Thomas Robinson, F, Kansas
6 Portland Trail Blazers (from Brooklyn) - Damian Lillard, G, Weber State
7 Golden State Warriors - Harrison Barnes, F, North Carolina
8 Toronto Raptors - Terrence Ross, G, Washington
9 Detroit Pistons - Andre Drummond, Center, Connecticut
10 New Orleans Hornets (from Minnesota via L.A. Clippers)- Austin Rivers, G, Duke
11 Portland Trail Blazers - Leonard Meyers, C, Illinois
12 Houston Rockets - Jeremy Lamb, G, Connecticut
13 Phoenix Suns - Kendall Marshall, G, North Carolina
14 Milwaukee Bucks - John Henson, F, North Carolina
15 Philadelphia 76ers - Maurice Harkless, F, St. John's
16 Houston Rockets (from New York) - Royce White, F, Iowa State
17 Dallas Mavericks - Tyler Zeller, F, North Carolina
18 Houston Rockets (from Minnesota) - Terrence Jones, F, Kentucky
19 Orlando Magic - Andrew Nicholson, F, St. Bonaventure
20 Denver Nuggets - Evan Fournier, G, Poiters Basket 86 (France)
21 Boston Celtics - Jared Sullinger, F, Ohio State
22 Boston Celtics (from L.A. Clippers via Oklahoma City) - Fab Melo, C, Syracuse
23 Atlanta Hawks - John Jenkins, G, Vanderbilt
24 Cleveland Cavaliers (from L.A. Lakers) - Jared Cunningham, G, Oregon State
25 Memphis Grizzlies - Tony Wroten, Jr., G, Washington
26 Indiana Pacers - Miles Plumlee, F, Duke
27 Miami Heat - Arnett Moultrie, F, Mississippi State
28 Oklahoma City Thunder - Perry Jones III, F, Baylor
29 Chicago Bulls - Marquis Teague, G, Kentucky
30 Golden State Warriors (from San Antonio) - Festus Ezeli, C, Vanderbilt