The 65-year-old said he was in a relationship with married Conservative activist Helen Harrison, who is 20 years his junior, after living apart from Mrs Bone for two years.
The backbencher and member for Wellingborough is a prominent Brexiteer and a key figure in the Leave Means Leave pressure group.
The former accountant has three children with his 57-year-old wife, who is also his constituency office manager and secretary.
But he said in a statement: “My wife and I have been living apart for more than two years, during which time I have formed a relationship with Helen Harrison.
“Neither Helen nor I intend to make any further comment about this matter.”
Mrs Harrison, 45, is married to builder Michael Harrison, of Corby, Northants, and has two children, aged 19 and 21.
The trained physiotherapist is a former Tory Parliamentary candidate and is a director, with Mr Bone, of Grassroots Out, a campaign to leave the EU backed by Nigel Farage.
Neither Mrs Bone, who underwent successful treatment for breast cancer 14 years ago, nor Mrs Harrison would comment yesterday.
Details of the marriage split emerged after Mr Bone was seen sharing intimate restaurant dinners in London with Mrs Harrison.
She is also understood to have stayed over at his £1.5million flat overlooking Westminster Cathedral on occasions.
In his 13 years as an MP he earned a reputation for his habit of mentioning his wife Jenny in risque jokes during political discussions – the MP mentioned her in at least 60 debates since he joined Parliament in 2005.
Former Conservative leader David Cameron appeared to be in on the “Mrs Bone” one-liners.
Following a weekend of successful Brexit talks, Mr Cameron once joked: “I take it even Mrs Bone is satisfied by the weekend’s activities – and that makes me a happy man.”