In an exclusive statement to PEOPLE, the Project Runway host and the singer say:
"While we have enjoyed seven very loving, loyal and happy years of marriage, after much soul-searching we have decided to separate.
"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. This is an amicable process and protecting the well-being of our children remains our top priority, especially during this time of transition.
"We thank our family, friends, and fans for their kind words of support. And for our children's sake, we appreciate you respecting our privacy."
The couple are parents to Leni, 7½, Henry, 6, Johan, 5, and Lou, 2.
The supermodel, 38, and the Grammy winner, 48, began dating in 2003 after Klum had split from Italian racecar team manager Flavio Briatore.
In December 2004, Seal proposed with a yellow diamond ring of more than 10 carats in a specially-built igloo on a 14,000-ft.-high glacier in Whistler, B.C. Klum described it as "a once-in-a-lifetime event."
They opted for a warmer destination for their wedding, exchanging vows on the beach in Costa Careyes, Mexico, in May 2005.