He said he will leave on August 31, seven years after he was first made chief executive, adding he had always intended to take on the role for that length of time.
Mr Delew said he looked forward to returning to Manchester permanently to be with his wife, children and their grandchild.
He wished Mr Gardner “every success” as his replacement.
CST chair Gerald Ronson said: “David has given his all for CST and our Jewish community, bringing focus, commitment and professional excellence across the charity.’
“I thank David, not only from CST and its trustees, but also on behalf of the whole Jewish community and our many allies in the continuing struggle against antisemitism.
“I wish David every happiness and success for the future. Looking ahead, I fear that Britain, Jews and CST will be facing difficult times, but in appointing Mark to lead CST, we have one of our community’s most experienced and highly respected professionals at the helm.”