Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
The former Barcelona coach was hired as an adviser nine months ago to help turn around the club's flagging fortunes but a first-round play-off exit this season does not appear to have impressed the club's owners.
The club released a statement which read: "The club has decided to terminate the services and consultancy with the company of Mr Johan Cruyff.
"This is because of not meeting the outcomes and objectives that have been established since the beginning of the contractual relationship.
"The coaching staff will not be affected, therefore technical director, trainer and technical assistants will continue to work with the club.
"The club thank Mr Johan Cruyff for the support and collaboration he has provided."