The order to deploy was given by the Defence Secretary Gavin Williamson, who in February confirmed the UK would be upping its contribution to NATO’s Enhanced Forward Presence.
It is the third time that Typhoons have been out to Estonia - the first was in 2015 and then again the following year.
Wing Commander Paul "Pablo" O’Grady, Officer Commanding XI Squadron said: "It's a really significant four-month period for XI squadron and for the Royal Air Force.
"Conducting Baltic air police missions over NATO countries is a key role for us as part of a NATO country, to reassure the Estonians, to deter any Russian aggression and to ultimately protect their skies.
"Next week we'll be taking over from the German Air Force - the German Typhoons which have been there for four months.
"Then starting off in a couple of weeks time we'll then be on quick reaction alert, much like in the UK, ready to get airborne in a matter of minutes to intercept any aircraft that should not be over Estonian airspace."
"So the team is obviously very well trained to deliver QRA [Quick Reaction Alert].
"We deliver it day in, day out from the UK, and we've done this mission before.
"We've done this mission in Estonia, we've done it elsewhere in Europe, so they're well-trained to go up and intercept and intervene aircraft if indeed any aircraft enter the airspace that they need to go and investigate."