Two of them are from Leeds, who became infected while travelling to Iran.
The third case, from Bradford, is not connected to the other two, Public Health England has confirmed.
Dr Simon Padfield, consultant in communicable disease control for Public Health England Yorkshire and the Humber, said: “Public Health England is contacting people who had close contact with three cases of COVID-19 confirmed in West Yorkshire.
"One of the cases is a resident of Bradford who became infected whilst in Italy and the other two cases are residents of Leeds who both became infected whilst in Iran.
"The case in Bradford is not linked to the two cases in Leeds.
"Close contacts will be given health advice about symptoms and emergency contact details to use if they become unwell in the 14 days after contact with the confirmed cases.
"This tried and tested method will ensure we are able to minimise any risk to them and the wider public.”