Oblak passed a medical on Thursday after agreeing to join Atleti on a six-year deal with the Spanish capital club a day earlier.
The Slovenian is likely to fill the void left by Thibaut Courtois, who is set to stay at Chelsea following three seasons on loan at the Vicente Calderon.
Atleti won La Liga for the first time since 1996 last season and also reached the final of the UEFA Champions League, only to lose 4-1 to city rivals Real Madrid after extra-time.
Meanwhile, Oblak won the Primeira Liga, Taca da Liga and Taca de Portugal for Benfica last term, but suffered heartbreak in the Europa League final as the Lisbon club were defeated by Sevilla on penalties.
And the 21-year-old is determined to win even more silverware with his new employers.
"I feel great, I'm really happy that I'm a new Atletico player and I'm really excited to start working here," Oblak told the club's official website.
"I spoke with [left-back Guilherme] Siqueira about the club, about everything, and he told me all the best and said that here it is great.
"I hope we will win a lot of trophies and I'm going to do everything for this.
"I will do everything for the club, I will always give 100 per cent and they can be sure about this."
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