Davis, previously of the Kentucky Wildcats, averaged 14.2 points, 10.4 rebounds and 4.7 blocks in the college circuit.
The school became the first one in history to go 1-2 as freshman Michael Kidd-Gilchrist was picked shortly afterwards by the Charlotte Bobcats. The Cats had to pass on Thomas Robinson for the opportunity, who was selected by Sacramento Kings instead.
“It’s crazy,” Davis said of the unique 1-2 scenario to ESPN.com.
"Michael is a great player. We have two down and four more to go. Hopefully all of them will go in the first round.
"I've wanted this all my life. So it's finally here. To be drafted No. 1 overall means a lot to me for a 19-year-old freshman — now a professional.
"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 four other players picked from the successful Wildcats team that won their 8th NCAA Tournament Championship were Terrence Jones, Marquis Teague, Doron Lamb and Darius Miller. Miller will join Davis at the Hornets in the coming season.
In addition to Davis and Miller, the Hornets also selected Austin Rivers in a tenth-round pick.
Dallas Mavericks carried out the most high-profile trades as they transferred Kelenna Azubuike and Tyler Zeller to Cleveland for the rights of Jared Cunningham (the 24th pick), Bernard James (the 33rd pick) and Jae Crowder (the 34th pick). The Mavericks are expected to save a great deal from Azubuke's salary and will be active in the free agency period which starts on Sunday.
Miami Heat, the winners of the 2012 NBA Finals, grabbed Arnett Moultrie in the 27th round while Oklahoma City Thunder, their opponents in the finals, signed on Perry Jones III.
The Los Angeles Lakers made the final pick as they snapped up Robert Sacre from Chicago Bulls via Milwaukee Bucks and Brooklyn Nets.