Patrick Clarke, 68, was stabbed several times at Southleigh Community Hospital in Brighton Road, Croydon, in May.
Jimmy Jedson, 40, a patient at Southleigh, was found guilty of manslaughter on the grounds of diminished responsibility.
Jedson was sentenced to a hospital order - which have no fixed end date - at the Old Bailey on Wednesday.
Det Insp John Massey, who led the Met Police's investigation into the attack, said: "The violent death of Patrick Clarke - a hardworking man who dedicated his life to helping others - is tragic."
"I can only hope that today's verdict goes some way to bringing closure to the victim's family who have behaved with the upmost dignity throughout this very harrowing ordeal."
A spokesman for Southleigh Community Hospital said: "Our deepest sympathies are with [Mr Clarke's] family, friends and colleagues.
"He was a valued and respected member of staff who will be deeply missed."
A patient has been convicted of stabbing a nurse to death at a private hospital in south London.