Jennifer Rennie, 26, was found dead at her home in Rosyth, Fife, yesterday morning.
The body of 41-year-old Scott Simpson was later discovered at his house about three miles away in Dalgety Bay.
Sources confirmed that Mr Scott is understood to have taken his own life after killing Ms Rennie.
The couple's five-year-old daughter and one-year-old son had been at their mother's home and are now being looked after by relatives.
It has emerged the couple had split up and Ms Rennie reportedly moved out of the family home several weeks ago.
Superintendent Gary Flannigan, of Fife Constabulary, said the incident looked to be "entirely self-contained" as police dealt with one death and one murder.
He said officers were not aware of any previous incidents involving the couple, who are thought to have had been together for about six years.
"We are dealing with a tragedy for two families," he said.
Mr Flannigan, of the Serious Crime Division, added: "Events began with a call to a house in Rosyth, and that led us to the house in Dalgety Bay.
"We are fairly confident we know what we are dealing with. There are two children at the centre of this tragedy."
The murder is the first being investigated by the Serious Crime Division, which was set up on March 5.
A neighbour of Ms Rennie alerted police to her death at about 7.45am on Monday and officers have been talking with residents of the two streets involved.
Superintendent Dougie Milton said: "We are providing reassurance to the communities at this time."
Two police officers stood guard outside Ms Rennie's home in Findlay Street, Rosyth. Floral tributes had been left at the pathway to the property. One contained a card which read "beautiful girl".
In a statement released through police, the family of Ms Rennie said: "Jenny was a loving mother, daughter, granddaughter, sister and friend.
"She was a friend to everyone and will be sorely missed.
"We are all devastated by what has happened and would now ask to be allowed some privacy to grieve at this sad time."
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