It said: "They treated a small number of patients on 4th and 5th February before they became unwell, followed advice and self-isolated".
He said today: "I'm happy to be home and feeling well".
In the United Kingdom a total of 1,358 people have been tested for coronavirus, of which eight were confirmed positive.
Professor Keith Willett, NHS strategic incident director, said Mr Walsh was discharged after two negative tests for coronavirus, 24 hours apart.
Yesterday a medical centre in Brighton was closed because two of its staff were confirmed as having the virus.
Mr Walsh released a statement from hospital revealing the steps he took to prevent the virus spreading further.
A statement on the website for County Oak Medical Centre - operator of previously closed Warmdene and Carden surgeries - told patients that the facilities have been "extensively and rigorously cleaned throughout".
One is in hospital after a man transferred from a Thai jail collapsed.
A British businessman who unwittingly spread the novel coronavirus as he traveled across the world is highlighting the challenges of containment in an interconnected world.
They include two Global Positioning System, one of them who has been named as Dr Catriona Greenwood, who owns the French chalet with her husband where others caught coronavirus from Mr Walsh.
Public Health England's Emeritus Medical Director Paul Cosford told Sky News earlier Monday that four new cases confirmed in Britain were "not a surprise" due to their links to a known case, believed to be Walsh.
The development came as at least nine schools in Brighton, Hove and Eastbourne in East Sussex informed families that some of their pupils or staff had been told to self-isolate.
The man, who was the first Briton to have tested positive for coronavirus, is in an isolation unit at London's St. Thomas Hospital and officials are on tracking down all the people he had contact with, especially those he travelled with on his United Kingdom return flight.
The 31-year-old was reportedly brought back to the United Kingdom two weeks ago after being extradited from Thailand.
He said one of those completed a locum shift at Worthing A&E last week and, as a precaution, the hospital has now "sent home for self-isolation a number of their staff from various departments of the hospital".
"My thoughts are with others who have contracted coronavirus", he added.