Suarez, 33, had one more year to run on the contract he signed with Barca in 2016 but was told by new head coach Ronald Koeman last month that he was not part of his plans.
He arrives at Atletico following the departure of Alvaro Morata, who rejoined Juventus earlier this week.
“I feel I’m capable of continuing to compete in this league,” Suarez said.
“When Barca told me they weren’t counting on me, there were many calls, many offers, but I was able to go to a team that can compete as equals with two great teams like Barcelona and Real Madrid. I had no doubts.”
Suarez departs Barcelona as their second-highest goal-scorer of all time, having scored 198 goals since signing from Liverpool in 2014.
He won La Liga titles, four Copa del Reys, the Champions League, the Club World Cup and the European Super Cup during his hugely successful time at the Nou Camp.
Suarez was filmed leaving Barcelona’s training ground in tears on Wednesday as his transfer to Atletico neared completion.
It was thought that Suarez was close to agreeing to terms with Italian champions Juventus but delays in obtaining Italian citizenship put the brakes on a potential deal.
Italian financial police and the Perugia public prosecutor’s office have since opened an investigation into allegations of irregularities regarding Suarez’s citizenship exam last week.
It is alleged that Suarez was aware of the contents of the exam before taking it and that his score was pre-assigned.
Juventus could not recruit Suarez without an Italian passport because they have already reached their quota for non-EU players.
