The 28-year-old Morocco star has not made a Premier League start for the Gunners since October 2011 and is yet to play in the top flight this season.
Hammers manager Sam Allardyce said: "We've struck a deal with Arsenal, I'm glad to say but unfortunately our registration went through too late and they've refused to allow him to be available for selection tomorrow (against Manchester United).
"I think that will be it in terms of strikers. We're due to get Andy Carroll back (to fitness) so we should be okay."
Chamakh arrived at The Emirates on a free transfer from Bordeaux in the summer of 2010 and, with Robin van Persie injured, began life in north London as Arsene Wenger's first choice striker.
But, after a positive start during which he scored 11 goals in his first 21 competitive games for the club, Chamakh's form slumped and he found the net just once in the remainder of his first season.
The towering forward struggled again in the 2011/2012 campaign, and although he recently notched twice in Arsenal's remarkable 7-5 Capital One Cup victory over Reading, has been allowed to move to Upton Park.
"I want to play and give my best for this team. I can bring my heading,
some goals and we will see what else," Chamakh said.
"I didn't have opportunities to play recently, but I did well before and I
know I am a very good striker.
"We played only one striker at Arsenal, so I didn't play a lot, so I hope to
do so more with West Ham."