Reports emerged on Saturday that the pair were to divorce amid claims the supermodel was fed up with her husband's 'hard partying'.
However, in an official statement this morning, the couple blamed their split on 'growing apart'
'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.'
After marrying at Seal’s beachfront home in Mexico in 2005, Seal and Klum kept their promise to renew their vows every year on their anniversary with their close friends and family.
They have three children together – Henry, six, Johan, five, and Lou, two – as well as Miss Klum’s daughter Leni, seven, from a previous relationship with Italian businessman Flavio Briatore.
And the tension in their relationship is believed to have started when the pair holidayed with their three children in Ibiza in August.
A source told the Sunday Mirror: 'They were always the couple everybody strived to be but lately it all started to change. Seal seems to have been partying a lot more often than usual.
'When they had their holiday in Ibiza last summer, Seal hit it hard, was out at clubs and with his friends a lot and Heidi was left with their kids trying to enjoy herself. The cracks were appearing and everybody was talking during that trip. He seemed off the rails.'
The insider added: 'They've spent a lot of time apart too on work assignments and that hasn't helped matters.
'Then when Seal came back to the UK to do promotional work for his next album, he seemed sleepy and not with it on shows like Loose Women, when he was very late for his appearance.'
And a source told The Sun today: '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.'
Further claims suggested that it was Seal's temper which led to the split, with a source telling TMZ.com that the singer's 'inability to control his temper' had a large part in the decision.
German-born Heidi, 38, is reportedly expected to file papers at Los Angeles’ County Superior Court this week citing 'irreconcilable differences'.
The message was attached to a picture that appeared to show the star’s forearm bearing an imprint of a set of wings – a possible reference to Miss Klum’s role as a Victoria’s Secret winged ‘Angel’ model.
The split paves the way for a multi-million-pound divorce battle between the golden couple.
Heidi, one of the world’s most in-demand models, is reported to have earned more than £12 million in the past year alone.
This is the relationship of Heidi Klum and Seal through the years:
May 2004: Heidi gives birth with Seal at her side
December 2004: Seal proposes in an igloo he had built on a glacier in Whistler, British Columbia
May 2005: The couple marry in a beach ceremony in Mexico
September 2005: Heidi gives birth to the couple's first son, Henry
May 2006: The couple start a tradition of renewing their marriage vows every year
November 2006: Heidi gives birth to their second son, Johan
October 2009: Their daughter Lou is born
September 2009: Seal officially adopts Leni
August 2011: The couple holiday in Ibiza, with reports emerging just this week that tension started during the trip because of Seal's 'hard parting'
December 26, 2011: The couple are last seen together, as Heidi tweets a picture of her and Seal on holiday in Aspen, Colorado
January 15th: Heidi attends the Golden Globes alone
Friday 20th January: Seal is seen arriving at LAX alone after a week in London promoting his new album
Saturday 21st January: Reports emerge the couple are to divorce
Today, Monday 23rd January: Heidi and Seal confirm they are separating, saying in a joint statement they have 'grown apart'