Under the terms of the deal, Porto have paid 11 million euros ($15 million) to acquire all of the 26-year-old's sporting rights and 60 percent of his economic rights, Porto said in a statement to Portugal's securities market commission.
There is also a buyout clause of 60 million euros, they added.
Adrian, who has two caps for Spain, joined Atletico from Deportivo La Coruna in 2011.
In three seasons with the club, he scored 26 goals in 142 appearances and helped them win their first La Liga title in 18 years last season and reach the final of the Champions League.
He also won the 2012 Europa League and the King's Cup and European Super Cup in 2013.