The 32-year-old Brazilian, who counts Porto, Atletico Madrid and AEK Athens among his former clubs, was a free agent after leaving Sao Paulo.
Assuncao has passed his medical with Depor and signed for the remainder of this season plus two more. There is also the option of a further season after that.
Assuncao said on his new club's website: "I'm very pleased, happy and grateful to come to a club as great as Depor and to be given the opportunity to return to Spanish football."
Depor last week installed Domingos Paciencia as their new coach following the sacking of Jose Luis Oltra. In his first match in charge, Domingos guided Depor to a 1-0 win over fourth-placed Malaga on Saturday, lifting the Galician club off the bottom of the Primera Division table.