The Pelicans picked Dawson at No. 56 last month.
The 22-year-old forward averaged 12.8 points and 10.3 rebounds while playing in four games for the Clippers at the recent Orlando summer league. He finished second in the standings in rebounding average and had a double-double in three of his games.
Dawson played four years at Michigan State, finishing as the school's career leader in blocks (142). He was a 2011 McDonald's All-American at Lew Wallace High in Gary, Indiana.
The deal was announced Wednesday.