Inter Milan have signed Brazilian defender Joao Miranda from Atletico Madrid.
Ipswich have signed winger Ainsley Maitland-Niles on a season-long loan deal from Arsenal.
The Spanish stopper put pen to paper on a deal that will keep him in Sardinia until the end of the season with an option to extend the contract for a further year, the Italian club confirmed on Wednesday.
The 26-year-old, who came through the Real youth ranks, became a free agent in June after the Madrid outfit failed to offer him a contract extension.
"I am delighted to be here," Adan said to cagliaricalcio.it.
"I wish to thank club president Massimo Cellino and the team for giving this opportunity."
Cagliari are 13th in Serie A and having given away 20 goals in 12 games.
The Sardinians travel to the Italian capital on Monday to face league leaders Roma.