"We're not looking at the Battle of LA. We've got bigger goals in mind," George said. "We're not thinking about the Lakers shadow. We want to be holding that trophy and we'll build up Clipper Nation along the way."
Leonard made the biggest free agent signing in the NBA this month by leaving the Toronto Raptors after leading them to the NBA title while George was obtained in a blockbuster trade deal with the Oklahoma City Thunder at Leonard's request.
"I'm on my next journey," Leonard said. "These guys have got a great future. Paul is a player I always wanted to play with. Both LA guys. Played down the street from each other. Now we're on the Clippers.
"We've got something speical. I think we can make history."
Clippers owner Steve Ballmer's high-octane introduction video became a quick social media sensation, the 63-year-old former Microsoft chief executive screaming and yelling his joy and excitement about his club suddenly becoming a prime NBA contender for the first time.
"I'm just fired up to be here today," Ballmer yelled. "It's pretty cool. It's pretty damn cool."
In a much more low-key manner, George and Leonard also showed their excitement about what the future has in store for them and the Clippers as they accepted blue Clippers jerseys, George number 13 and Leonard number 2.
"I'm extremely happy and extrmely excited to be back home," George said after thanking the Thunder for making the trade deal. "Ultimately they helped me find my way back to LA. I'm pretty appreciative of that."
- Clippers outshine Lakers lately -
The Clippers are second favorites among Caesar's Palace sportsbook NBA championship oddsmakers at 7-2, trailing only the 3-1 odds for the Los Angeles Lakers, who boast LeBron James and Anthony Davis plus a host of solid support talent after being unable to add Leonard to their own lineup.
The Lakers have won 16 NBA titles but none since 2010 with retired star guard Kobe Bryant as the NBA Finals Most Valuable Player.
Leonard instead chose a Clippers' squad that has never gone past the second round of the NBA playoffs, never reaching even a conference finals since being formed in 1970 as the Buffalo Braves.
But in each of the past seven seasons, the Clippers won more games than the Lakers, a trend Leonard plans to continue.
"The last few years, the Clippers have been better," Leonard said. "They are going to get the attention -- the Lakers have been winning championships for a long time.
"Who knows how the Clippers will change things over? I'm not focused on that. I just want to win. My goal is just to make us happy. If we're winning and not getting no coverage, that's fine with me."
Asked about the growing power of NBA players under contract to force teams into trade deals, George said, "As long as there's a mutual respect between both (club and player), there's nothing wrong with it."
- Inspiring next generation -
George hopes that with both players being among the NBA's top defenders, the Clippers will alter dynamics to bring more attention to two-way work than simply scoring skills.
"What me and Kawhi can do is inspire the next generation, go out and play hard on both ends," George said.
The Clippers' existing core was attractive to Leonard and George.
"Everybody elevated their games. To be part of that camaraderie, what they already had, to sprinkle in what we have to offer, that's what made it such an attractive spot," George said.
Leonard was happy the team kept contract talks from leaking to the public.
"They were true to their word. Nothing got out," Leonard said. "I just felt like it was a good decision for me.
"It's a good pairing. They go hard both ways. They want to win. That's my competitive mindset when I step on the floor. I'll pass the ball to someone else. That's the culture here.
"It's going to be a team effort. It's going to take 15 guys to make this work."