The Nigeria striker has been searching for a new club since cancelling his contract with Turkish side Gaziantep at the end of last month.
Ameobi was linked with a move to West Brom, but he has instead opted for a reunion with Palace boss Alan Pardew, with whom he worked at Newcastle United.
The 33-year-old came through the youth ranks at St James' Park and went on to score 79 goals in 397 first-team games for the club.
Speaking on his move, Ameobi told Palace's official website: "I'm very excited to be here, I wanted to get back in the Premier League and having worked with the manager before it's been great to come back and hopefully help us avoid the relegation battle.
"I had a couple of other clubs interested but I think my relationship with Alan and how much I enjoyed working with him was one of the big factors in my decision.
"He instils confidence in players and he always seems to get the best out of them, certainly he did that at Newcastle and hopefully he can do that for me and the rest of the lads here."
