According to the Associated Press' Tim Reynolds, Wade and Riley hugged and made amends last month at the funeral service for Wade's former agent, Henry Thomas.
"The hug that we embraced was real and it was all we needed," Wade said, per Reynolds. "That's it. That's all we both needed. I walked away and I felt better about everything, without even getting into anything."
Wade and Riley's relationship was previously put to the test in July 2016 when the 12-time All-Star bolted for the Chicago Bulls on a two-year, $47 million deal after he turned down a two-year, $40 million offer from the Heat.
"It was a sad day when Dwyane left, and it's a beautiful day now that he's back," Riley told reporters on a conference call after the trade was finalized.
"It's about competing for a favorable playoff spot or even just to get into the playoffs. That's what this is about. And I couldn't think of a better player to bring in here without having to give up a lot of assets or young assets...to be able to get Dwyane back to help us in that role, I think it was a very good deal for us."
Wade will return to Miami as a bench contributor after starting 845 of 855 games during his first 13 years with the franchise.
"Don't matter," he told Reynolds. "I can't wait to embrace whatever role I have."
Wade is expected to be in uniform Friday night when the Heat host the Milwaukee Bucks at American Airlines Arena.