The FAW did not reveal the circumstances of the death of the 42-year-old former midfielder.
“The Football Association of Wales are sad to announce the death of the national team manager Gary Speed,” read an FAW statement.
“We extend our sympathies and condolences to the family.
“We ask that everyone respects the family’s privacy at this very sad time.”
A spokeswoman for Cheshire Police said: “At 7.08am today, Cheshire Police was informed of a sudden death at an address in Huntington, 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. The family have requested that they are left in peace to grieve at this difficult time. A family tribute will be released at a later date but not today.”
Speed had been in charge of the national team since December 2010, and had recently presided over a run of four wins in five internationals to climb to 50th in the world rankings.
Speed had previously served the Welsh national team with distinction as a player, winning 85 caps in a 14-year international career.
His greatest moment at club level came in 1992 when he won the championship with Leeds, while he was twice an FA Cup runner-up with Newcastle.
Speed also represented Everton, Bolton and Sheffield United in 22-year professional career which saw him make nearly 700 league appearances.
He also held the record of most Premier League appearances with 535 until 2009 when veteran goalkeeper David James overtook him.
He retired from playing in 2010 before embarking on his first managerial role with Sheffield United.
Speed, who was awarded the MBE in the 2010 Birthday Honours for his services to football, leaves a wife and two children.
GARY SPEED TIMELINE
1969: Born on September 8 in Mancot, Flintshire.
1988: Signs professional terms with Leeds, making his debut at the age of 19.
1992: Plays a key role as the club win the First Division title in the last season before it was rebranded as the Premier League. Leeds’ midfield of Gordon Strachan, David Batty, Gary McAllister and Speed was hailed as a key factor in their success.
1996: After 312 appearances for the West Yorkshire side, during which he scored 57 goals, Speed completes a £3.5million move to Everton. He went on to be named captain of the Toffees and made 65 appearances over two seasons, scoring 17 goals.
1998: February - Joins Newcastle for £5.5million.
May - Plays in United’s FA Cup final defeat to Arsenal.
1999: Speed suffers further FA Cup disappointment as Newcastle lose a second successive final, this time to Manchester United.
2002: Plays in the Champions League with the Magpies.
2004: Joins Bolton for £750,000.
2006: December - Becomes the first player to make 500 Premier League appearances when he features in Wanderers’ 4-0 win over West Ham.
2007: May - Named as Bolton’s first-team coach after Sam Allardyce resigned as manager.
August 25 - Speed’s goal against Reading makes him the only player to have scored in every Premier League season to date. The achievement was later matched and extended by fellow Welshman Ryan Giggs.
October - Returns to playing duties, with new coach Sammy Lee claiming the decision was his while Speed insists he resigned.
December 24 - Sheffield United agree deal to sign Speed on loan from January 1, with a view to a permanent £250,000 move.
2008: November - A back injury ends Speed’s season, leaving him to concentrate on a coaching role.
2009: June - Approached by Swansea over the possibility of succeeding Roberto Martinez as manager.
2010: May 6 - Formally announces his retirement as a player, though he was registered and named as a substitute for August 11’s League Cup tie with Hartlepool.
August 17 - Appointed Sheffield United manager on a three-year contract as successor to Kevin Blackwell.
October 21 - Handed one-match touchline ban by Football Association after being charged in relation to an incident during October 2’s home defeat to Watford.
December 13 - United give Speed permission to speak to the Welsh FA over vacant role of national team coach. Speed takes up the position the next day.
2011: February 8 - Takes charge of Wales for the first time, beating the Republic of Ireland 3-0 in the Carling Nations Cup.
March 29 - Loses first competitive match 2-0 to England at the Millennium Stadium.
September 2 - Records first competitive win, 2-1 at home to Montenegro.
November 12 - Records third win a row and fifth in seven matches in his last game in charge - a 4-1 friendly victory over Norway.
November 27 - The Football Association of Wales confirm he has died.