BA’s CityFlyer operation will launch the service on Saturdays and Sundays until June 20, Edinburgh Airport confirmed to The Scotsman.
It is expected to operate using 98-seat Embraer 190 aircraft.
Portugal is expected to be among the few European countries which people from the UK may be permitted to visit from Monday May 17 without the need to quarantine after returning.
However, they would have to undergo pre-flight Covid testing.
An announcement on the list of countries is expected from the UK Government tomorrow.
The Scottish Government has said it was working towards a four UK nations approach to the partial lifting of international travel restrictions.
A traffic light system will denote the risk levels in each country and measures required to be taken by travellers.
An Edinburgh Airport spokesperson said: “There is pent-up demand for travel, and airlines are already showing confidence in Edinburgh Airport by providing new routes and capacity, and that is extremely encouraging.
"Clearly, we have to wait to find out what the new Scottish Government wishes to do, but we are clear that a four-nations approach is needed or Scotland will lag behind the rest of the UK and Europe and suffer significant job losses across the country as a result."
British Airways has been approached to provide a comment on its plans for the flights.