The couple's representatives announced that they briefly split three years ago but reunited shortly, after which Brancaccia harassed the Italian producer.
The news was out in the open as they were involved in a police investigation, The Times reported.
"Subsequently, Mr Brancaccia carried out a frightening campaign of harassment over several months, much of which is documented. For obvious reasons, the Firths have never had any desire to make this matter public," the statement from Firth and Guiggioli read.
Brancaccia has denied stalking Guiggioli and has claimed she wanted to leave Firth "for me".
The couple married in 1997 and have two children Luca, 16, and Matteo, 14.
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