Dr Helen Nicoll, 53, was found dead at home in Frog End, Great Wilbraham, Cambridgeshire, on Friday.
Her husband and partner in their dental practice, Stephen Nicoll, 53, was arrested on suspicion of murder before being released on Tuesday.
A post-mortem examination revealed Mrs Nicoll died from asphyxiation.
Mr Nicoll was released by police with no further action and his bail cancelled.
The couple had three children and worked together in their clinic in Hurst Park, Cambridge while Mr Nicoll also practises in London's Harley Street.
Mr Nicoll said in a statement: "These last few days have been the worst of my life.
"Nobody can understand the true loss that my children and I have experienced following the discovery that my wife Helen has taken her own life.
"I would ask everybody, particularly the media, to respect our privacy and allow us to come to terms with our devastating loss and to begin the grieving process as a family following this tragedy."
He added his family had "fully co-operated" with police and his wife's death had been referred to the coroner.
Mr Nicoll's solicitor Paul Oliver said: "The arrest of Mr Nicoll in the immediate aftermath of the death of his beloved wife and the consequential media interest in this tragic case compounded the distress caused to him and his family.
"The police have confirmed Mr Nicoll is not a suspect and he and his family now ask that their right to grieve in private be respected."
The husband of a dentist who was arrested over her death has said she "took her own life" as he told of his family's "devastating loss".