The 42-year-old father-of-two was found dead at his home on Sunday morning.
A spokeswoman for the coroner, Nicholas Rheinberg, confirmed her office had been informed of the death by police.
The inquest will be opened at the coroner's court at Warrington town hall before a full hearing takes place at a later date.
Speed was found by his wife, Louise, in the garage of their home in the village of Huntington, near Chester, shortly after 7am on Sunday.
Police said the death was not being treated as suspicious.
Supporters have left scarves, football shirts and flowers across several football stadiums - including Everton's Goodison Park, Leeds' Elland Road, Newcastle's St James' Park and the Millennium Stadium and Cardiff City Stadium, where Wales played their home games.
The FAW has opened a book of condolences at its offices in Cardiff allowing fans to express their feelings about Speed's death.