Griffin did not get a no-trade clause as part of the new contract, sources told ESPN's Ramona Shelburne.
Griffin met with team owner Steve Ballmer, president and coach Doc Rivers, special consultant Jerry West and several players at Staples Center on Friday. One person involved reportedly described the meeting as "a trip down memory lane," with players Jamal Crawford, DeAndre Jordan, Patrick Beverley, Wesley Johnson and Sam Dekker all featured in a "production."
At the end of the two-hour fete, Griffin rose and spoke, telling teammates, his coach and the owner that "I want my legacy to be a Clipper."
An emotional scene ensued, and many among the group, including Rivers and Ballmer, went out to dinner afterward, sources said.
A teammate of Griffin's, who spoke to ESPN on condition of anonymity, said he had always worried that Griffin was impressionable enough to make an emotional decision in the moment and perhaps sign with Miami, Boston, Phoenix or elsewhere during free-agency courtship.
Griffin reportedly had been scheduled to meet with the Suns and Denver Nuggets once free agency started Saturday.
"We've had some great meetings with them and love the direction of the organization," a source close to Griffin told ESPN's Royce Young. "Feel that the best chance to win is definitely with LAC."
The agreement was first reported by The Vertical.
The 6-foot-10 Griffin had previously told the Clippers he would decline his player option for next season.
Griffin is recovering from a toe injury that has left him questionable for the start of the season. He suffered the injury to the plantar plate of his right big toe in Game 3 of the Clippers' playoff series loss to the Utah Jazz.
In the 2016 playoffs, he suffered a quad injury in Game 4 of the Clippers' first-round series against the Portland Trail Blazers. He did not return for the remainder of that series, and the Clippers were eliminated in six games.
In a podcast earlier Friday with USA Today's Sam Amick, Lawrence Frank, the Clippers' executive vice president of basketball operations, talked about Griffin's importance to the team.
"The perception of the Clippers changed once Blake Griffin started as a Clipper, right?" Frank said. "And we've had great success.
"Chris obviously, you know, was great -- Chris' winning ways, we're grateful for [them]," Frank said of Chris Paul, whom the Clippers traded to the Houston Rockets this week. "But Blake is in a position where we look at him as Clipper royalty, and it hasn't changed. So we are going to do everything we can to keep Blake a Clipper."