The first four years are guaranteed, and the fifth year is a team option, according to ESPN.
The team will make a formal announcement within 24 hours, the Vertical reported.
Lue, 39, led the Cavs to that NBA title after taking over for David Blatt in January. He never signed a contract as a head coach and was working on a four-year deal worth $6.5 million as Blatt's top assistant when the Cavaliers won three straight over Golden State to capture the title.
His four-year deal made him the highest paid assistant in the league.
The Vertical reported that he left a three-year, $9.5 million contract offer on the table during the season, a move that ultimately is paying off.
Lue compiled a 27-14 record down the stretch in the regular season. The Cavaliers swept the Detroit Pistons and Atlanta Hawks before needing six games to eliminate the Toronto Raptors in the Eastern Conference finals.
Lue played 11 seasons in the NBA after he was the Denver Nuggets' first-round pick in 1998 out of the University of Nebraska. A point guard, he averaged 8.5 points, 3.1 assists and 1.7 rebounds in a total of 554 games (173 starts) for the Los Angeles Lakers, Washington Wizards, Orlando Magic, Houston Rockets, Atlanta Hawks, Dallas Mavericks and Milwaukee Bucks.