The moves, announced by the club Tuesday, are formalities for players chosen in the first round. The values of their rookie deals are outlined in the NBA's collective bargaining agreement.
As the first pick in this summer's draft, the 6-foot-11 Davis receives a three-year guaranteed contract worth a little more than $16 million, with just over $5 million paid in the first year.
Rivers, a 6-4 guard picked 10th overall, receives a three-year guaranteed deal worth nearly $5.9 million, with nearly $1.9 million paid during his rookie season.
The Hornets' second-round pick, 6-8 forward Darius Miller, still must negotiate his contract. Generally, contracts for second-round picks are not fully guaranteed.