Cubero makes the move to Bloomfield Road from Herediano in his homeland for an undisclosed fee and has put pen to paper on a one-year contract with the option of a further 12 months.
The 27-year-old, who featured for his country at the World Cup in Brazil, told the club's official website: "I am very happy to sign for Blackpool, it is a dream come true.
"It is a very nice stadium and it's my first chance to play abroad. It has always been a dream to play in England and grow as a footballer, so it's a great opportunity."
Cubero, a holding midfield player, has won 39 caps for Costa Rica.