The England all-rounder has settled his differences with the county and a club statement said it was hoped Cork would continue as captain "for many years".
Last month Cork put in a written request to be released from his contract after his demands that two committee members be ousted were rejected. The former chairman Vic Brownett resigned because of the power struggle.
Cork also claimed a "dirty tricks campaign" was being run within the club against him after it was reported he had abused Trevor Bowring, the newly appointed chairman. But Cork said yesterday: "I am happy that all the differences have been sorted out, and we have a structure that we feel can allow me to concentrate all my efforts into leading Derbyshire into a successful future."
A club statement said: "Following discussions with committee members Les Elliott and Trevor Bowring, and latterly with the secretary, previous problems have been resolved with a thorough examination of the way in which cricket is run at the county.
"As a result, a structure has been put in place to ensure that it creates clear and professional management guidelines for the running of first- class cricket at Derbyshire.
"A cricket committee, composed of a chairman selected to work with the captain, the captain himself, the vice-captain, the second XI captain, plus the new post of cricket manager, will have total authority over professional cricket, within a set budget. The position of cricket manager will be filled shortly."
Meanwhile, Andy Hayhurst, Derbyshire's director of coaching and development, has left the club by mutual consent.
A statement from the club said: "The club would like to thank Andy for his services to Derbyshire and the valuable contribution he has made during his time at the club."
During his playing career Hayhurst captained Somerset and also turned out for Lancashire.Reuse content