Former fast bowler Holding, 63, was part of the Windies' feared attack during the 1970s and 80s and played for Derbyshire for six seasons from 1983.
Morgan, who replaces Chris Grant, was named at the club's AGM on Wednesday.
Holding, who took 249 Test wickets, said his new role was a "great honour".
He added: "I enjoyed immensely the few years I spent at Derbyshire and I always enjoy returning.
"On my last visit in September, I saw all of the facilities, all of the improvements and the infrastructure which has gone into the club.
"I am sure that the progress made off the field and around the ground will transfer onto the cricket field and that we will see some good results this summer."
Media playback is not supported on this device
West Indies legend Michael Holding has been appointed as president of former club Derbyshire, who have also named local businessman Ian Morgan as their new chairman.