Team president Glen Grunwald said Martin will be signed to a 10-day contract with the hopes that he could stay with the team for the remainder of the season.
Grunwald said Martin will be insurance for injured big men Rasheed Wallace and Marcus Camby, a pair of 38-year-old backup forwards who have both been battling foot injuries.
"We've always liked Kenyon, he's a great competitor and good defender," Grunwald said on a conference call, adding that Martin was already familiar with many Knicks. "We think that there will be some synergies already built into the mix and we're just looking forward to adding a good defender who can help us in our quest this season."
Martin played with Carmelo Anthony, J.R. Smith and Camby in Denver before spending last season with the Los Angeles Clippers, averaging 5.2 points in 42 games. He also teamed with Jason Kidd in New Jersey on teams that reached the NBA Finals in 2002 and 2003.
But Martin, 35, has been injury prone in recent years. Still, he's a rugged and versatile defender whom Grunwald thinks can help.
"We watched a lot of the tape of his season last year with the Clippers and he played very well," Grunwald said. "We're hopeful that he's going to show that he's still got what it takes to be an NBA player."
Brewer was a starter earlier this season who lost his spot - and eventually his place in the rotation entirely - after a shooting slump. He was dealt for a 2014 second-round pick and cash.
Brewer was phased out once Iman Shumpert returned from knee surgery. Never much of a scorer, Brewer had played well during the Knicks' strong start, but never recovered once things started to go bad and Grunwald didn't really know why.
"I'm not really sure, but he obviously was not playing and we just tried to look at what our team needed to move forward," Grunwald said.
Grunwald said Brewer didn't demand a trade, and said the team didn't consider moving Shumpert, who has struggled since returning from his torn knee ligament and whose name was linked to various rumors.
Brewer appeared in 46 games, making 34 starts, and averaged 3.6 points and 2.2 rebounds. Signed by New York last summer, he has also played for Utah, Chicago and Memphis.
Grunwald wasn't certain if Martin would be available when the Knicks face Philadelphia on Sunday, saying it may not be until next week.