The new arrangement will see Colin Metson taking on a manager director position with the cricketing decisions being taken jointly by chairman Paul Russell and chief executive Alan Hamer as well as new overseas player Alviro Petersen taking over as captain.
Walker, a lifelong Glamorgan man who played 469 first-class games and three Tests over a 17-year career, is unhappy with the developments and admits he has concerns with their potential impacts.
"Much has already been reported on the proposed changes in the running and structure of the team," said Walker. "I have serious concerns about their likely impact. My standing down now will give the Chairman and officers of the club sufficient time to recommend a suitable replacement to the membership.
"Throughout my period in office the loyal fans of Glamorgan overwhelmingly gave me their support. They deserve, and will expect the new president to continue to speak and act on their behalf.
"In the 17 years I played for the county, Glamorgan were a club to whom I was totally committed, on and off the field. That state of mind remains and I'm proud of my Honorary Life membership for services to the club - and the game of cricket."
Dalrymple had joined Glamorgan from Middlesex at the end of the 2007 season and was made captain in 2009. "I have today [Thursday] resigned from Glamorgan County Cricket Club with immediate effect," he said in a statement. "I have done so because Glamorgan have effectively dismissed me by removing the captaincy from me, recruiting a new post above Matthew Maynard and me, recruiting a new overseas player and captain in Alviro Peterson.
"All of this without consultation or prior notification with me. This has rendered my position at the club untenable. The first I knew of any of these fundamental management and cricket decisions was on Monday afternoon when the chairman Paul Russell phoned to inform me of a fait accompli," he added. "I understand the club's right to remove the captaincy at their discretion and I recognise that the results in one-day cricket are not yet at a level we were happy with."