Young, who averaged 11.8 points and 6.3 rebounds this season, had considered the possibility of entering the free-agent market.
The Pacers could enter free agency with as much as $20 million in salary cap space.
Young, 30, played a leadership role for the young Pacers, who earned the fifth seed in the Eastern Conference playoffs and pushed the Cleveland Cavaliers to a seven-game series in the first round.
Young averaged 11.3 points, 7.7 rebounds and 1.7 steals in the series against the Cavaliers.
For his career, which spans a decade with Philadelphia, Minnesota, Brooklyn and Indiana, Young has averaged 13.4 points and 5.9 rebounds.