Speed, who joined the Blades as a player on New Year's Day 2008 and spent a brief spell as manager in 2010 before leaving to take on the Wales coach's job, was found dead on Sunday morning.
"Everybody at Sheffield United is extremely shocked and saddened to learn of the death of former player and manager Gary Speed," read a statement from the League One club.
"Thoughts are with Gary's family and friends at this distressing time.''
The 42-year-old's playing days ended at Sheffield United and he enjoyed a role as first-team coach before being appointed as Kevin Blackwell's replacement as manager in August 2010.
But his spell as boss at Bramall Lane was short-lived as he left South Yorkshire for the job of Wales coach in December 2010.