The youngsters, one aged 10 and 13, were left to fend for themselves while their mother attended a family wedding in Nigeria.
It is understood they had continued to go to school while she was away but when officers visited the home, they found the house was in an unkempt condition while the children had no food or heating.
The mother, who lives in Salford in Greater Manchester, has since been arrested on suspicion of child neglect and her children were taken into care.
Police said she had left the family home on January 28 to fly out to the wedding and had intended to stay out of the country until next week.
But she flew back to the UK early on Wednesday after being alerted that the authorities were investigating. The woman was arrested at London’s Heathrow Airport and questioned before being bailed.
The children, who were found at home by officers with no food, no heating and with the house in a state, have since been taken into the care of Salford Council (pictured is their headquarters at Salford Civic Centre)
A Greater Manchester Police spokesperson said: “A woman has been arrested on suspicion of child neglect.
“She was arrested at Heathrow Airport on February 11, 2015 and bailed until March 19, 2015.
“Her two children are now in the care of the local authority.”
A Salford Council spokesperson confirmed the children had now been placed with a foster parent.