The 34-year-old was a free agent, having left Palace in June after seven years at Selhurst Park.
"They're exciting times and I'm excited to start working with the lads," said Hennessey, who is Wales' most-capped goalkeeper.
"Popey's a great lad but it's competition, which is healthy," Hennessey said.
"That's part of the goalkeeping union. There's always competition. There's always that one spot but we'll be friends off the field.
"There's a fantastic spirit here and hopefully we'll do really well this season."
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