The pair - who have three children together - confirmed their break up in a joint statement shared on social media, saying they "still have a great relationship" and still share a home.
It comes amid rumours that the pair's relationship was on the rocks.
The statement said: "We hadn't planned on sharing this publicly until we were ready but the lack of privacy surrounding our personal life, we feel left with no other option but to clarify.
"A while ago we took the difficult decision to separate but our main focus was as always is to continue loving and supporting our children.
"This was not an easy decision to make but we're moving forward as the best parents we can be for our three beautiful children."
"We'll always be a loving family, we still have a great relationship and still live happily in our family home together," they went on.
"We hope this now draws a line under anymore unwanted and unnecessary intrusion into our private life.
"Although we work in the public eye we ask kindly if you could respect our wishes for privacy on this matter."
They added that they would not be making any further comment.
Christine, 34, and Top Gear presenter Paddy, 48, tied the knot in June 2011 and have three children together - nine-year-old twins Leo and Penelope and six-year-old daughter Felicity.
Leo and Penelope were diagnosed with autism in 2017, and in 2020 the family were told that their youngest daughter also had the disorder.
Last year, Christine was diagnosed with autism at the age of 33 and has said it helped her to understand herself better.
Rumours of relationship problems started swirling in recent weeks, and Christine told The Sun earlier this month: "I can’t deny we are having a very, very difficult time.”
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