The Football Association of Wales (FAW) has told the BBC it appears Speed, the national manager for nearly a year, killed himself.
Cheshire Police confirmed he was found dead at 07:08 GMT at his home in Huntington, Chester. They said there were no suspicious circumstances.
First Minister Carwyn Jones called it "devastating news" and said he was deeply saddened.
He said: "Our thoughts are with his family at what must be a very difficult time for them."
The FAW said: "We extend our sympathies and condolences to the family. "We ask that everyone respects the family's privacy at this very sad time. That this tragedy should have overtaken someone so young and talented is a huge loss not only for his family and friends but a nation as a whole."
Speed, who was awarded the MBE in the 2010 Birthday Honours, leaves a wife and two children.
Phil Pritchard, FAW president, said they would do "whatever we can" to help Speed's family.
In a statement, Cheshire Police said: "At 7.08am on Sunday 27th November Cheshire Police was informed of a sudden death at an address in Huntington in Chester.
"Officers went to the scene where a 42-year-old man was found dead.
"The next of kin have been informed and have confirmed the identity of the man as Gary Speed.
"There are no suspicious circumstances surrounding the death and the family have requested that they are left in peace to grieve at this difficult time."
Police said a family tribute will be issued later.
RIP Gary Speed, a true premier league legend. British Football has lost one of the true greats.