It said the deployment was part of an “increased presence in the region” and was requested by the host nations.
The UK signed mutual security assurance declarations with both countries in May. They are also both members of the UK-led Joint Expeditionary Force, a coalition of 10 nations.
Defence Secretary Ben Wallace said: “Finland and Sweden are important defence partners and we welcome their applications to join NATO, which will make the alliance stronger as we face a renewed threat in Europe.
“These deployments highlight our determination to enhance that partnership and ensure our forces can work together seamlessly.”
Two F-35Bs and four Typhoons conducted “high-end warfighting training” with Finnish F-18 Hornets and Swedish Gripen aircrafts, the RAF said.
Swedish defence minister Peter Hultqvist said the joint exercises “strengthen our ability to operate together in response to a crisis in our neighbourhood”.
“This is particularly important in today’s challenging security environment.”