Rakip, who moved to Benfica from Malmo earlier this month after making 30 appearances for the Swedish champions last season, has 11 caps for his country's under-21 team.
"I believe this is a league that suits me and my way of playing," the 21-year-old told Palace's website (www.cpfc.co.uk). "It's fast-paced and physically intense, and I'm a... box-to-box player who runs up and down the field."
Former England manager Hodgson managed at Malmo in the 1980s, leading the club to five consecutive league championships.
"It will be an honour playing for Roy. He is a legend in Malmo and everyone knows who he is," Erdal said. "It feels amazing arriving to the best league in the world and to be part of a great team."
Hodgson replaced the beleaguered Frank de Boer at Palace early in the season, taking over with the club at the bottom of the table and without a point after four straight defeats.
The 70-year-old has since steered the side out of the relegation zone and up to 13th in the standings ahead of their trip to 11th-placed West Ham United on Jan 30.