The centre-back has spent the last two seasons with Malaga and made 40 appearances last term as the club reached the quarter-finals of the Champions League.
But after turning down the offer of a contract extension with los Boquerones, Demichelis has opted to join last season's third-placed Liga side and spoke of his ambitions for the season ahead shortly after putting pen to paper.
He told Marca: "I know that I'm joining the best defence in the league and 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.
"I know that Miranda and [Diego] 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."
The 32-year-old then admitted the influence of Atleti boss and compatriot Diego Simeone had swayed his decision to join los Rojiblancos and snub both Malaga and River Plate.
"It was a difficult decision because two clubs to which I am eternally grateful, River and Malaga, wanted to sign me," he added.
"I went to Argentina and I was thinking about staying there, but then Atletico appeared and Simeone was key in convincing me to join a consolidated group that was playing for trophies.
"Simeone has known about me for a long time and is aware of my performances in the last few years. He is one of the main reasons I'm now an Atletico player."
After selling Radamel Falcao to Monaco earlier this summer, Atleti have bolstered their ranks in recent weeks with the renewal of goalkeeper Thibaut Courtois' loan for a third successive season and the signings of Leo Baptistao and David Villa.