Cassell's agent, David Falk said that his client had signed the necessary paperwork and will bring it with him when he flies to Boston on Tuesday.
"He had some personal business he had to attend to in Baltimore. There was a death in the family," Falk said, according to the Boston Globe. "But he will be on his way up there and everything is done. He is really excited."
The team wasn't ready to say the deal was official.
"We anticipate him being a member of the Celtics," team spokesman Jeff Twiss said. "He is not a member of the Celtics until he signs, which will not be until he gets into town sometime [Tuesday]."
Cassell was virtually begging to be let go by the Clippers, who owed him $6.1 million this season in the final year of his contract, and be signed by the Celtics. He got his wish on Thursday, when Los Angeles bought out his contract and waived him.
Whether he suits up for Wednesday night's game against Eastern Conference rival Detroit is up to coach Doc Rivers, Twiss said.
"He's a proven player," Rivers said, according to the Globe. "We're just going to wait and see where he fits in on our team. He's coming in with the right frame of mind and he just wants to help. He knows how to play. He's terrific at the end of games. He can still really play."
Cassell's arrival comes a week after Boston, which has the NBA's best record (46-12) signed big man P.J. Brown. Brown, who had been out of the league this season, has not suited up for a game yet.
The 38-year-old Cassell missed four straight games with a sprained right wrist before being cut loose by the Clippers; he also missed 12 games earlier in the season with a strained left calf. In 38 games, Cassell averaged 12.8 points, 4.7 assists, 2.8 rebounds and 25.7 minutes.
Cassell was a member of the Houston Rockets teams that won NBA titles in 1994 and '95. His best season with the Clippers was in 2005-06, when he averaged 17.2 points and 6.3 assists and helped them move within a game of the Western Conference finals.
In Boston, he will be reunited with Kevin Garnett, his former teammate in Minnesota.
Rajon Rondo appeared to be in favor of adding a player who could potentially take some minutes away from the second-year point guard.
"[Celtics GM Danny Ainge] asked me how I felt about it," Rondo told the Boston Herald. "I told him I thought it would be a great idea. It can only help me."
Information from The Associated Press was used in this report.