The Magic send center Bismack Biyombo to the Hornets, where he started his career as the No. 7 overall pick in 2011.
Chicago acquires Charlotte guard Julyan Stone, who has a non-guaranteed contract that could be waived next month.
The Magic, who have not had a winning record or made the playoffs since the lockout-shortened 2011-12 season, get salary-cap help in Grant's $2.69 million expiring contract, while Mozgov's deal has two years, $32.7 million left.
For the Bulls, Stone's $1.65 million contract has an Aug. 1 guarantee date. If Stone is waived, Chicago's cap space would increase to $16 million in room -- assuming forward Noah Vonleh's hold is released.
For Charlotte, Biyombo has two years, $34 million left on his contract. The Hornets have $120 million in salary and are $3.4 million under the luxury tax threshold with 14 guaranteed contracts on their roster.
ESPN's Bobby Marks contributed to this report.