Striker Stead, who scored 20 goals in three season at Ashton Gate, is aiming for a move back up north while Skuse, who has spent his entire nine-year career with the Robins departs after 307 appearances.
While City wanted to keep the duo, they have let the short-term deals for Mark Wilson, Brian Howard and Matthew Bates expire. Goalkeepers Dean Gerken and Lewis Carey will also leave the club as they prepare for npower League One football.
"We wish all of the players who are leaving the football club well for the future," new director of football Keith Burt said.
"With Cole, he's been an exemplary servant for this football club and we fully understand his reasons for moving on at this time in his career.
"For Jon the lure of playing back up north has been too strong and we wish him luck for whatever his future career holds."
City also confirmed their intention to extend the contracts of Tom Heaton, Lewin Nyatanga and Louis Carey.
"The head coach believes Tom and Lewin would be key players for us in League One next season and we'll be making offers to them both," he said.
"With Louis, his experience and know-how is seen as important for what we believe will be a young squad."
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