INDEPENDENCE, Ohio — They have an unmatched chemistry on the floor, a connection that has led to NBA championships, Olympic gold, worldwide fame and strengthened an unbreakable bond.

LeBron James and Dwyane Wade aren’t just friends.

More like family — basketball brothers.

“It’s like peanut butter and jelly, man, we just go together,” Wade said.

Reunited with the Cavaliers after their four-year run with the Miami Heat ended with an abrupt split after two titles, Wade and James are again teammates, a fact that neither of them can believe.

“Every time we walk by each other in the locker room and everywhere, we just look at each other and shake our head because it just don’t seem real,” Wade said Friday. “It’s like, ‘How did this happen? How did we get here?’ We just start laughing every time we walk by each other.

“It wasn’t planned, it wasn’t expected, but when it happened it happened and everything happened fast. It’s definitely cool. It’s definitely good to have a friend here, somebody that you respect here, that’s playing the game here.”

Here. Cleveland.

Surreal.

Wade, who signed a one-year, $2.3 million contract Wednesday with the Cavs, was introduced by the team on Friday following a practice. The workout didn’t include James, who rolled his left ankle during Wade’s first workout with the team and is being listed as day to day with the injury.

Wade posed for photos holding his new No. 9 Cavs jersey, and the 35-year-old said he already feels at home in a place that has usually been welcoming, even when James famously bolted from Cleveland as a free agent in 2010 to join he and Chris Bosh in South Florida.

When he arrived earlier this week, Wade found himself in familiar company: James, Cavs assistant coaches and former teammates James Posey and Damon Jones, and players he’s battled with over the years like Derrick Rose, Kyle Korver and Richard Jefferson.

From the outset, it just felt right.

“I’ve been around Bron, I’ve been around this organization for a while from afar, so I knew everybody,” Wade said. “I knew the coaches. It was seamless. I was telling my family. It was just like, just get me a jersey and I just got out there and it felt normal. It felt seamless. That made me at ease.”

The three-time champion and 12-time All-Star smiled often and joked some during his first formal get-together with Cleveland’s media, swollen beyond the normal number.

Wade made it clear that his decision to come to Cleveland — spurning offers by Miami, Oklahoma City and others — wasn’t solely to play again with James. Obviously, that was a major factor, but Wade said he was mostly driven by an internal desire to get back in the meaningful game where he has always thrived — on the biggest stage, where careers are defined.

Two seasons removed from his last Finals, Wade recalled a game in Indianapolis where he scored just 5 points.

“Everybody said I was done, and I was this and that and then I came back the next couple of games and scored 30, 28 and 41,” he said. “I miss that. “I miss being in my room not talking to nobody, feeling like the world is on my shoulders and then coming out and showing what I’m made of.

“I haven’t had that in a couple of years so getting an opportunity to be back on this team and understanding — knock on wood everybody stays healthy — what we can accomplish, you know, those moments are going to come.”

Wade’s playing role is still to be determined. Cavs coach Tyronn Lue, who has the unenviable job of keeping players unaccustomed to coming off the court happy, has had him playing point guard with Cleveland’s second unit.

Entering his 15th season, Wade isn’t concerned about how much he’ll play or where. His only focus is doing whatever Lue asks.

“It’s everybody’s job that has on a Cleveland jersey to be ready and prepare for whatever he decides and we’re deep,” he said. “I don’t want to peg anybody against anybody, especially because I’m here. If someone’s starting then they’re starting and it’s your job to come in when they come out of the game and do your job.”

James had been recruiting Wade for months, starting this summer when Chicago traded Jimmy Butler, a sign the Bulls were in rebuilding mode. So once Wade, who estimated he has given up on nearly $30 million in his career to play for championships — “I’ll go on record and say that I’ve given back the most money in the NBA” — completed a buyout from his $23 million contract, James contacted his close friend and convinced him the Cavs should be his choice.

Wade got strong pitches from Paul George and Carmelo Anthony to join the Thunder.

He was flattered, not swayed. Cleveland had something more — James.

“At the end of the day this is where I wanted to be,” Wade said. “This is where I felt I should be from a basketball perspective to come in and be a part of this.”