Sources said Jefferson, who committed to re-sign with the Dallas Mavericks earlier this month, changed his mind in recent days and is finalizing a one-year veteran minimum deal with the Cavaliers instead.
The move will add some wing depth for Cleveland, which could potentially strengthen the Cavaliers' bargaining position as they continue to haggle with the unsigned J.R. Smith, who opted out of the final season of his existing contract (valued at $6.4 million) to become a free agent July 1.
Jefferson's return to Dallas was initially considered such a formality that the 35-year-old joined owner Mark Cuban and starting small forward Chandler Parsons at a July 3 celebration of the Mavs' ill-fated verbal agreement with marquee free agent DeAndre Jordan.
But Jefferson's free agency has since played out in a similar fashion to Jordan's, with a U-turn on his intention to sign with Dallas to return to the Eastern Conference with the title-chasing Cavs.
When reached Tuesday, however, Cuban said that he actually spoke to Jefferson about his change of heart and was not blindsided by the decision as Dallas was in Jordan's case.
"He called and talked to me," Cuban told ESPN. "RJ said he had an opportunity with an Eastern Conference team. He said he would honor what he [originally agreed to with the Mavs] but thought the other was a better fit. I told him I was OK with it and understood."
As of Tuesday, Cuban and Jordan still have not communicated directly since Jordan decided on July 8 to walk away from a four-year max deal with the Mavericks worth in excess of $80 million to stay with the Clippers.
Jefferson, meanwhile, averaged a mere 5.8 points per game for the Mavericks last season, but the 14-year veteran sports a career scoring average of 13.9 points after some strong years with the then-New Jersey Nets.
The Cavaliers will be his fifth team in the past five seasons. Cleveland, though, is bound to find some opportunities for Jefferson, who has registered better than 40 percent marksmanship from 3-point range in four of the last five seasons, including a success rate of 42.6 percent in 2014-15 with Dallas.