Jefferson, who turned 36 on June 21, finished his 15th season by making his third career appearance in the NBA Finals. He averaged 17.9 minutes and 5.5 points in his first season in Cleveland but started Game 3 of the championship series and had nine points and eight rebounds in place of the injured Kevin Love.
"He's a true professional, and a guy who is seizing an opportunity and moment to be in this position," LeBron James said after the Cavs beat the Warriors in Game 3 to cut their series deficit to 2-1. "The last time he was in the Finals was his first and second year in the league [in New Jersey], and I think he's not taking this moment for granted.
"He knows his role. He plays it very well, and he's key to our team."
Jefferson went on to play key minutes the remainder of series, helping Cleveland win its long-awaited championship.
Afterward, he said he was contemplating retirement.
"Maybe. If you ask me now, yes. But we'll see," he told ESPN.
Jefferson has averaged 13.3 points over his career, including a career-best 22.6 points per game with the Nets in 2007-08.
Information from ESPN's Ohm Youngmisuk was used in this report.