Clyne was out of contract at Selhurst Park but he will still command a fee because of his age. The two clubs are still in discussions over compensation and an independent tribunal will decide the fee if an agreement cannot be reached.
Adkins said there were more signings to come, telling the Daily Star Sunday: "It is fair to say we are going to need to bring another goalkeeper in as Bartosz Bialkowski did ever so well for us but didn't play enough games.
"We've allowed him to move on to Notts County and will bring in another one, if not two goalkeepers, while we will be looking to bring in another couple of centre-halves as well."
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