ESPN.com reported the Cavs came to terms with Korver on a three-year, $22 million contract.
The 36-year-old Korver joined the Cavaliers after a trade with the Atlanta Hawks during the middle of last season but never gave the team the offensive boost off the bench it sought, particularly in the postseason.
In 35 regular-season games, Korver averaged 10.7 points and shot 49 percent on 3-pointers. In the playoffs, those numbers fell off to 5.8 points per game and 39 percent from 3-point range.
In 67 regular-season games split between Cleveland and Atlanta, Korver averaged 10.1 points and 45.1 percent on 3-pointers.
After the loss to the Golden State Warriors in the NBA Finals, Korver expressed a desire to remain with Cleveland.
Signing Korver will add to the Cavaliers' luxury tax bill. According to ESPN.com, the third year of Korver's contract is only partially guaranteed per the new collective bargaining rules.
The 6-foot-7 Korver has career averages of 10.7 points and 43.1 percent shooting from 3-point range.
NBA free agent contract cannot be signed until a league-wide moratorium ends Thursday.
The Cavaliers likely aren't finished making moves. There are reports that the team is shopping Iman Shumpert.