Paddy Bowden was discovered in the couple’s former shared house in Chiswick, west London, around 10am on Monday morning.
Mr Dickinson said in a statement: “This is a terrible tragedy which appears to be a tragic accident.
“Our children Austin, Griffin and Kia and I are devastated.
“Out of respect for Paddy we won’t be making any further comment at this hugely difficult and painful time for our family.”
London Ambulance Service said they were called to the house on Monday morning.
A spokesperson added: “We sent two ambulance crews to the scene – the first one arriving within two minutes.
“Sadly, the patient had already died.”
Mr Dickinson and Ms Bowden married in 1990 after a two-year relationship. They split up in 2018.
Ms Bowden is survived by her three children with Mr Dickinson, who are all in their twenties.
Iron Maiden formed in east London in 1975 and became one of the largest heavy metal bands in the world.
The band has sold more than 100 million albums worldwide.