The 33-year-old midfielder, who left Pescara last season, played alongside Seedorf at the San Siro Stadium in 2012.
"I had offers, but I chose to come here because it's a club that was in the Champions League," Muntari told the club's website.
"They have the DNA of a big club, historic and with a winning mentality.
"It was easy to choose, because also there is an old team-mate [Clarence Seedorf] who is the coach," he added.
Muntari made his debut on Sunday against Espanyol in jersey No.21, which was previously donned by the club's legend Juan Carlos Valeron.
"I don't know him. Was he a good player? If he was a legend, then it will be a big responsibility for me," he added.
Deportivo sit 19th on the 20-team log, with Muntari expected to start his first game against Getafe on Wednesday.