Young is back on a four-year, $21.3-million contract with a player option on the final season.
Kelly received a two-year contract for $3.4 million. The Lakers can once again make him a restricted free agent in 2016.
The Lakers used $1.65 million of their $2.73 million "room exception" on Kelly, leaving $1.08 million still available to spend in free agency -- although that amount remaining is actually less than a minimum salary for a veteran with at least six years of experience.
The organization currently has $55.4 million in official salaries for eight players (Kobe Bryant, Steve Nash, Jeremy Lin, Carlos Boozer, Julius Randle, Robert Sacre, Young and Kelly). The Lakers have also agreed to re-sign Jordan Hill to a two-year, $18-million contract (second season team option) along with forwards Ed Davis, Wesley Johnson and Xavier Henry, each at a minimum salary.
Even unsigned, Hill takes up $6.8 million in salary cap space.
Second-round pick (46th overall) Jordan Clarkson, who has yet to sign, will increase the roster to 13 players. The Lakers can carry 15 players to the regular season, although a maximum of 20 can be taken to training camp.
While over the cap, the team can still sign players on minimum contracts.
Barring a trade, the Lakers are unlikely to hit $70 million in total salary, well below the NBA's punitive luxury tax line at $76.8 million.