The former Republic of Ireland international had two playing spells with Coventry before his retirement in 2011, when he was appointed to the League One side's coaching staff.
However, following a two-year stint, Carlsey has decided to take up a position alongside his former Everton teammate David Weir at Bramall Lane.
"Lee has been a highly valued and tremendously popular figure among both the club's players and staff and I have certainly enjoyed working with him since I arrived here," said Coventry manager Steven Pressley.
"I do though fully appreciate that this opportunity is one he could not turn down and I wish him nothing but the best of luck and offer my heartfelt congratulations on his new role."
Carsley, 39, had a brief caretaker spell in charge of Coventry last season before Pressley was appointed.