The 32-year-old passed a medical on Thursday and then spoke to reporters about the move, saying: "I'm very proud to have joined such a successful and winning group. Next year the team will compete even more than last season and there are many challenges to face."
Demichelis, who has also played for River Plate and Bayern Munich, joins an Atletico defence which conceded the least goals in La Liga last season, and will have to fight Diego Godin and Miranda for a regular place in the starting line-up.
"I know that I'm joining the best defence in the league I hope we can keep that up. I will come here with a humble attitude and will contribute what I can. I hope it's a successful year for me and for the team," he added.
"I know that Miranda and Godin have a huge amount of respect in the team, they have both performed exceptionally well in the last few years.
"My career has never been easy and I've always had healthy competition for places."