The details of the agreement would be revealed later on Tuesday, the representative said.
La Vanguardia newspaper said that, according to the agreement their children Milan, 9, and Sasha, 7, will move to Miami with their mother.
Shakira, 45, and Pique, 35, were together since 2011 but they never married.
They met shortly before the 2010 World Cup in South Africa when he featured in the music video for Shakira's "Waka Waka (This Time for Africa)", the tournament's official song.
They made public the end of their relationship in a June statement.
The custody agreement was reached one week after Pique announced his imminent retirement from professional football and his departure from FC Barcelona.
The "Hips Don't Lie" singer is facing a trial over alleged tax fraud charges in Spain after she lost an appeal on May 26.
Prosecutors claim she failed to pay up to 14.5 million euros ($14.48 million) in tax on income earned between 2012 and 2014.