Davis, the first overall pick in the 2012 draft, averaged 13.5 points, 8.2 rebounds, 1.8 blocks and 1.2 steals and was named an NBA All-Rookie First Team member last season.
The 6-foot-10 former Kentucky star was a regular starter at power forward. His 20 double-doubles led all rookies.
Rivers was the 10th overall pick in the draft. He averaged 6.2 points, 2.1 assists and 1.8 rebounds, but saw his rookie campaign cut short by a hand injury in early March, during a game in which he'd scored 10 first-half points against the Los Angeles Lakers.
The Pelicans announced the moves, which were expected, on Wednesday.
