Alan Shearer said he would "miss him dreadfully", and Ryan Giggs said he was "one of the nicest men in football".
Welsh and English politicians also paid tribute, with First Minister Carwyn Jones saying he was "deeply saddened".
Alan Shearer Former Newcastle teammateGary was a magnificent person... he lit up every room he walked into”
"It goes without saying my thoughts are with his family at this tremendously sad time."
Another of Speed's former Wales teammate, Robbie Savage, tweeted: "The world has lost a great man in Gary speed I'm devastated spoke to him yesterday morning why ! Why. Why !! I'll miss him so much x
"He come to watch strictly [Strictly Come Dancing] 3/4 weeks ago I high fived him in the front row he loved the show ,he loved life he loved his family ! Devastated".
Alan Shearer, who played alongside Speed at Newcastle for six years between 1998 and 2004, said: "Gary was a magnificent person, bright, fun and a wonderful family man - he lit up every room he walked into.
"I am proud to have been his friend and will miss him dreadfully."
Liverpool manager Kenny Dalglish released Welsh international striker Craig Bellamy from his squad for Sunday's match against Manchester City, saying Bellamy "was very, very close to Gary".
First Minister of Wales Carwyn Jones said he was deeply saddened, adding: "This is devastating news and our thoughts are with his family at what must be a very difficult time for them."
Welsh Secretary Cheryl Gillan tweeted: "This is a sad day for football and for everyone in Wales. Gary Speed served club and country as a player and manager with great distinction."
Andrew RT Davies, Welsh Conservative leader, said he and millions of others "will always remember him as a legend in the game of football".
Welsh Liberal Democrats leader, Kirsty Williams, described the death as a "tragedy for the Speed family and a tragedy for Welsh football."
Plaid Cymru leader Ieuan Wyn Jones said the "whole nation is in shock."
"He will never be forgotten," he added.
Other politicians paid their respects, with a Downing Street spokesman saying: "The prime minister was deeply saddened to hear of the death of Gary Speed, who was greatly respected by football fans across the country both as a player and manager.
"The prime minister's thoughts are with his family and friends on this very sad day for fans everywhere, especially in Wales."
Labour leader Ed Miliband tweeted: "Tragic and shocking news about Gary Speed. Fantastic servant of Leeds. Mourned by football. Deepest condolences to his family."
A spokesman for BBC Sport said: "The news of Gary's death is a huge shock. Our thoughts and sympathies are with his friends and family at this incredibly sad time."
A statement from the Welsh Rugby Union said: "Wales has lost a great sportsman, a true gentleman and a man who was working extremely hard and succeeding to deliver a bright future for Welsh football."
Cheshire Police were informed of a sudden death early on Sunday morning, and found Speed dead at the property.
A statement added there were no suspicious circumstances and the death is now being dealt with by a coroner.
Speed, born in Mancot, Flintshire, had appeared on BBC1's Football Focus show on Saturday afternoon, just hours before his death.
He began his playing career at Leeds United after coming through the trainee ranks, and was part of the side that won the last Football League title in 1992, before the introduction of the Premier League.
A Leeds spokesman said the club was "stunned and saddened" by the news.
Newcastle followed, in a £5.5m switch in 1998. During his six years with the Magpies, he suffered two FA Cup final defeats, but enjoyed a taste of Champions League football.
He then spent four years with Bolton Wanderers after agreeing a £750,000 move and finished his playing career at Sheffield United, retiring at the end of the 2009-2010 season.
Speed, who was the first player to reach 500 Premier League appearances, also won 85 caps for his country - a record for an outfield player.
He made his international debut as a 20-year-old in the 1-0 friendly win over Costa Rica in May 1990 and his final appearance for Wales was in a 3-2 World Cup qualifying defeat against Poland in October 2004. He captained his country 44 times and scored seven goals.
He took over the Wales job in December 2010, despite having just four months' managerial experience, but the team had started to make impressive progress under his stewardship.
A 4-1 friendly win over Norway earlier this month represented a third successive win for Wales, and Speed's fifth in 10 games as manager.
At the time, he said: "We've progressed further than I'd have thought in this space of time but we've still got a lot of work to do."
In the 2010 Birthday Honours list, Speed was awarded the MBE. He leaves a wife and two children.
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