The pair split in January after seven years of marriage, though Seal had expressed hope for a possible reconciliation in the future.
While Klum filed for divorce on April 6, the 'Kiss From a Rose' singer has since begun his own proceedings, citing irreconcilable differences as the reason behind the break-up.
According to Access Hollywood, Seal filed for joint legal and physical custody of the former couple's four children, going against Klum's request for sole custody.
Last month, Klum confessed that she was in a "tornado of emotion" following her split from Seal.
Seal has said that he felt fans deserved an explanation about his separation from the Project Runway host.