The global sportswear brand has pinched the prolific frontman from Nike five months before the start of the World Cup in Brazil.
"I'm delighted to sign with Adidas who are the true leaders in global football," 101greatgoals.com quotes Costa as saying.
"The brand has a fantastic history but they are also at the forefront when it comes to innovation, which is why I was drawn to them so much. I look forward to great success wearing Adidas boots and I'm proud to join the group of other great players Adidas sponsors."
Costa is believed to have attracted a number of clubs around the Premier League and Europe having netted 20 goals in 22 games in La Liga.