Davis and Kidd-Gilchrist -- members of a Kentucky team that rolled to the NCAA championship last season -- were chosen 1-2 by the New Orleans Hornets and Charlotte Bobcats.
Davis, 19, earned consensus player-of-the-year honors in college basketball. In his only season with the Wildcats he averaged 14.2 points and 10.4 rebounds per game. He blocked a school record 186 shots.
New Orleans won the draft lottery last month even though the Hornets had a mere 13.7 percent chance of capturing the top spot. The franchise has drafted No. 1 only one other time, that coming in 1991 when Larry Johnson of Nevada-Las Vegas was the top choice.
Kidd-Gilchrist also played only one season for Kentucky. He scored 11.9 points and claimed 7.4 rebounds per game to go with 39 steals and 37 blocked shots.
The first five selections were rounded out by Washington taking Florida guard Bradley Beal, Cleveland choosing Syracuse guard Dion Waiters and Sacramento settling on Kansas forward Thomas Robinson.
This was the first time in NBA Draft history that freshmen were chosen with the top three picks.
After Robinson, the next five players selected were Weber State guard Damian Lillard (Portland), North Carolina forward Harrison Barnes (Golden State), Washington forward Terrence Ross (Toronto), Connecticut center Andre Drummond (Detroit) and Duke guard Austin Rivers (New Orleans).
Rivers is the son of Boston Celtics Coach Doc Rivers.