Odom agreed to return to the Lakers, but Kupchak noted that the contract negotiations "took many twists and turns." Odom called it "a tedious time."
Still, Kupchak and Odom were finally together at the team's El Segundo training facility.
"I guess it's a little late to ask him for a little bit more," joked Odom, who then signed his contract -- a four-year deal worth about $33 million, with a team option for the final year.
"You can ask," Kupchak answered, getting laughs from reporters.
Odom acknowledged he kept weighing his options, "even today when I woke up."
Yet despite interest from the Miami Heat that Odom described as aggressive, the lure of winning another championship with the Lakers prevailed in the end.
"At this point in my career, all I want to do is win. That's how we're going to be remembered, as winners or losers. Right now I want to be remembered as a winner," Odom said.
The deal capped off a busy month for the Lakers. Free agents Ron Artest and Trevor Ariza essentially switched places, with Artest going to the Lakers and Ariza to Houston.
The Lakers also waived guard Sun Yue, 23, who played in only 10 games last season as a rookie and spent part of the season on the team's Development League squad. The Lakers had until Aug. 1 to exercise their option on Sun. He would've earned $736,000 next season had the Lakers kept him.
Sun, a 6-foot-9 guard from China, was the Lakers' second-round pick in the 2007 NBA draft.
After Odom signed and Sun was waived, the Lakers had 13 players under contract. And Kupchak said it was likely the team would open training camp with that number.
"We're where we want to be as a team," Kupchak said. "We brought back basically everybody that we hoped to bring back."
That includes Odom, who can play both forward positions and fill in at center, and whose versatility made him a key component of the Lakers' 2008-09 championship season.
After Odom became a free agent on July 1, the Lakers presented him with two offers, each worth about $30 million guaranteed.
Then owner Jerry Buss took the offers off the table because Odom and his agent, Jeff Schwartz, didn't respond quickly enough.
And though Odom said Friday that Buss' move was just "bluffing," he also acknowledged that it hit a chord.
"That was the first time in my life since I was 8 years old where I wasn't picked to play," Odom said.
Odom said he talked to Buss and the owner explained his concerns about the Lakers' and the NBA's luxury tax threshold, which dropped from $71.15 million last season to $69.9 million next season.
That's when Odom said he decided to tell Buss directly that the money issues were his least concern, even if the prolonged discussions created a different impression. "It makes me feel awkward when I have to pitch myself," Odom said.
"I let him know how important it was for me as a person to be a part of his franchise, why I love L.A. so much. All I could tell him was the truth."
In the end, Odom sounded relieved.
He also said that he's looking forward to the future.
"If we can win six, seven, eight, nine, 10 championships in a row, I want to experience that," Odom said.