Wilcox is out for the season as he prepares for aortic surgery on March 29.
Celtics president of basketball operations Danny Ainge, who confirmed Thursday that the deal was nearly done, said Hollins came highly recommended by both Paul Pierce and Kevin Garnett, who worked out with the Los Angeles-area native this summer during the lockout.
It is unclear whether the 27-year-old Hollins will be available for the Celtics for Friday night's game in Philadelphia against the 76ers.
The 7-foot Hollins, who was waived by the Cavaliers earlier this week, averaged 3.7 points and 2.3 rebounds per game for Cleveland this season in just more than 15 minutes per game. He played in 24 games, seven of them starts, before being waived earlier this week.
With both Wilcox and Jermaine O'Neal (wrist) out for the season, the Celtics desperately need a legitimate big man.
Offensively, the Celtics will have to figure out a way to get Hollins going toward the basket. He thrives in the pick-and-roll and off putbacks, which could make him a natural candidate to set high screens for Rajon Rondo and Boston's ballhandlers, then attack the basket.
On defense, Hollins' length and athleticism allow him to contest shots and hold his own defending the pick-and-roll. However, his rebounding numbers are not exceptional, as he has averaged 2.2 boards per game in 299 NBA games.
It will be interesting to see how Rivers distributes minutes between Hollins and rookie center Greg Stiemsma, who is showing steady development. While the Celtics want to encourage Stiemsma's growth, he is also nursing a lingering right foot injury and could benefit from rest.
The question is whether Hollins -- and anyone else the team brings in before Friday's deadline for playoff eligibility -- can pick up the playbook quick enough for Rivers to develop confidence in him.
But the Celtics just need a big body to eat minutes, so it's likely Hollins will get tossed into the fire -- and his level of play will determine how much he plays over the final 20 games of the season.