The couple - who raise four children, Leni, seven, Henry, six, Johan, five, and two-year-old Lou, together - admitted while they "continue to love each other very much", they have "grown apart".
They said in a statement: "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."
Despite the split, the couple - who tied the knot at Seal's beachfront home in Mexico in 2005 - explained "protecting the well-being" of their children continues to be their "top priority".
They added: "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."
While the German supermodel is expected to file divorce papers at Los Angeles' County Superior Court this week citing irreconcilable differences, she reportedly split from the 'Kiss From A Rose' hitmaker "months ago".
A source told The Sun newspaper: "The marriage ended months ago in reality. They rarely saw each other and it wouldn't be unusual for them to go months without spending any real quality time together. Ships that pass in the night would be an overstatement."
Heidi, 38, and Seal, 48, met in 2004 when the model was pregnant with daughter Leni from her previous relationship with Italian businessman Flavio Briatore.
Hmmm, what's this movie with Josh Hartnett and Rachael Leigh Cook on the cover?...
"Blow Dry" is a leaden British dramedy about an estranged family of hairdressers reconciling when...