A petition, which lists irreconcilable differences as the reason for the split, was filed Friday afternoon in Los Angeles Superior Court, PEOPLE confirms.
Klum is seeking joint legal custody, but primary physical custody of their four children – Leni, 7½, Henry, 6½, Johan, 5, and Lou, 2 – with visitation rights for Seal. The model is also requesting to have her maiden name restored. She legally changed it to Seal's last name, Samuel, though professionally she continued to use Klum.
"While we enjoyed seven very loving, loyal and happy years of marriage, after much soul-searching, we have decided to separate," the couple previously said of their split. "We have had the deepest respect for one another throughout our relationship and continue to love each other very much, but we have grown apart."
Rumors first swirled that Klum, 38, and Seal, 49, were planning to divorce the day before they made the announcement. For the couple who married in Mexico in 2005, the split played out in headlines as the end of a fairy tale as both Seal and Klum gradually stopped wearing their wedding rings.
Although multiple sources told PEOPLE that the couple hoped to reconcile, by mid-February it was clear a reunion would not be in their future after all.
Seal was vocal about their split in the weeks following their announcement.
"When you publicize your marriage as much as our marriage was publicized, when you renew your wedding vows, when you do all those things, what you are saying to people is … you're giving people a picture of an ideal relationship that people aspire to," the British singer explained in February.
"When it goes south, you can't all of a sudden take the philosophy of a monk and decide to go for a vow of silence."
The quieter Klum acknowledged in the April issue of Elle that she couldn't control what Seal said to the press, but "it's hard."
"People don't need to know who did what," she said. "I don't want to talk positively or negatively about the ups and downs that we had."