Sharp steps up from a role as 2nd XI and batting coach, but he will not have the same authority as Rhodes as Worcestershire's restructure reasserts that overall charge rests with the chief executive: Matthew Rawnsley, a businessman and former spin bowler with the county, was appointed last month.
The former Worcestershire pace bowler Alan Richardson returns to the county as bowling coach - a role that he lost at neighbouring Warwickshire after their relegation in the Championship last season.
Matt Mason has also been reshuffled. He now takes charge of the 2nd XI in addition to overseeing a number of outreach coaching programmes involving young player and coach development.
Sharp's appointment brings a homely conclusion to a period in which Worcestershire were linked with such exotic choices as Graeme Hick, the former England batsman, who had a prodigious career with the county but who is now settled in Australia.
His appointment reflects the county's desire for continuity as the team seeks to build on the development of a young but rapidly maturing group of English-qualified players in which Rhodes took such pride and who held him in such high regard.
Rhodes was forced out after his failure immediately to report rape allegations that had been made against a 2nd XI batsman, Alex Hepburn, until after the player had been charged.
Sharp's considerable coaching experience was primarily with Yorkshire until he was part of a coaching cull carried out by the then chairman Colin Graves, now chairman of the ECB.
During his time, Yorkshire unearthed a host of batsmen who went on to play for England, including Joe Root, the England Test captain, Jonny Bairstow and Adam Lyth.
After a spell coaching Shropshire, Sharp joined Worcestershire in 2014.
Sharp said: "I am honoured and privileged that the club think of me in this way in awarding me this position. It was unexpected but I will do all I can to help Worcestershire be successful."
Richardson took more than 250 wickets in just four years for Worcestershire and Sharp said he has much to offer as a coach.