Buss is controlling owner and president of the Lakers and has described Bryant as like a member of her family.
Pelinka too was very close to the late NBA superstar, serving as his agent for many years before taking the front office role with the team.
"Kobe, I don't know how to express what you mean to me, my family and the Los Angeles Lakers," Buss wrote on Instagram. "My father loved you like a son, which makes us family."
She recalled when her father, team owner Jerry Buss, died in 2013, Bryant was one of the people who gave her strength and purpose. Kobe, she said, brought Gianna to see Jeanie "to show her that women can be leaders in the NBA, just like the men."
"At first, it seemed like an action of a devoted father setting an example for his daughter. But in actuality - and I am positively sure you knew EXACTLY what you were doing - what you did was give me the inspiration and strength I was searching for. I reflect on that day often and it makes me smile and it makes me strong."
She encouraged Bryant fans to help the other families affected by Sunday's helicopter crash by visiting MambaOnThree and to further Kobe and Gianna's legacy in youth sports by visiting Mamba Sports Foundation.
Pelinka put out a statement that read in part:
"On Sunday, I lost my best friend and my sweet goddaughter. With that, there has been an amputation of part of my soul.
Kobe was a force of nature, deep and obsessed with excellence. He was wise, determined, passionate. A visionary beyond measure. A dedicated and loving husband, and a "girl-dad" like no other. When he walked into a room, the energy ignited. He was high voltage, with a motor that had no limits. His mind had an infinite capacity to learn. He was, simply put, the most inspirational athlete of our time. What the world may not know, is that he was also the best friend anyone could ever imagine."
The tributes were issued even as Bryant fans continued to descend on LA Live to pay their respects and share memories and while Staples Center is preparing for basketball.
The Clippers play Thursday night and the Lakers play Friday.
"Kawhi (Leonard) said something really cool: If I know one thing about Kobe, he would want us to go out here and bust our ass. Be competitive, be a pro. That helped put things into perspective and loosen up," said Clippers player Landry Shamet.
"They will be doing something briefly before the game so people can all share that moment together and then the game will get on because there is an opportunity now to get back to one's normal schedule, one's normal routine. The players need to do that as much as the fans do," said Michael Roth, VP of communications for AEG, owner of Staples Center.
"It goes back to Kobe - Mamba Mentality. Stay focused. Know what Kobe would want. He would want us to win this for him, play the best basketball. He would want the Lakers to do their best," said Kobe fan Carlos Stallworth.
"You play because it's what Kobe would have wanted. He was relentless. He taught us about work ethic and what it meant to be a champion, on and off the court. You play because you want to keep his legacy going," said Christy Nickerson, a Kobe fan from Cleveland, Ohio.
Meanwhile -- the investigation into the crash that killed Kobe Bryant is moving forward.
Investigators are sifting through the wreckage at a secure location in Phoenix. The National Transportation Safety Board is expected to release its preliminary report next Friday.
And Mayor Eric Garcetti says he is working with Kobe's family on a public memorial.
Vanessa Bryant spoke up for the first time about her husband on Wednesday, thanking the public for support and sharing the family's grief.
She wrote: "We are completely devastated by the sudden loss of my adoring husband, Kobe - the amazing father of our children; and my beautiful, sweet Gianna - a loving, thoughtful, and wonderful daughter, and amazing sister to Natalia, Bianka, and Capri."
We are also devastated for the families who lost their loved ones on Sunday, and we share in their grief intimately."