The film-star couple issued a statement yesterday saying they had drifted apart.
"It is with great sadness that we have decided to separate. Our work has inevitably led to our spending long periods of time away from each other and, as a result, we have drifted apart.
"The separation is entirely amicable but, as with the breakdown of any relationship, it is painful for both of us and we ask the media to respect both our privacy and that of our friends and families."
Mr Branagh, 34, best known for his numerous Shakespearean roles, has moved out of the couple's London home and is lodging temporarily at the house of his personal assistant, Tamar Thomas, according to some newspaper reports.
One reason for the break-up is said to be the work schedules that both actors have taken on over the past two years.
Miss Thompson, 35, who won an Oscar for her role in the Merchant Ivory epic Howard's End, has made five films in that time and she reportedly checked into a luxury health clinic earlier this year suffering from exhaustion.
She is the daughter of Phyllida Law, the classical actress, and Eric Thompson, narrator of The Magic Roundabout.Reuse content