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Johnson signed the new declarations, described by Britain as "a step-change in defence and security cooperation", during visits to both Sweden and Finland on Wednesday.
"What it says is that in the event of a disaster, or in the event of an attack on either of us, then we will come to each other's assistance, including with military assistance," Johnson said at a news conference in Helsinki.
Russia's invasion of Ukraine has forced a rethink of how Sweden - and neighbour Finland - safeguard national security.
Both are expected to join NATO, but both are worried they would be vulnerable while their applications are processed, which could take up to a year.
Asked if Finland would be provoking Russia by joining NATO, Finnish President Sauli Niinisto said Russian President Vladimir Putin would be to blame for any decision to join the military alliance.
"My response would be that you caused this. Look at the mirror," Niinisto said.
Sweden has also received assurances of support from the United States and Germany.
Speaking earlier alongside the Swedish Prime Minister Magdalena Andersson, Johnson said: "The war in Ukraine is forcing us all to make difficult decisions. But sovereign nations must be free to make those decisions without fear or influence or threat of retaliation."
Britain said the new arrangements would intensify intelligence sharing and accelerate joint military training, exercises and deployments.
Johnson said the nature of any assistance will "depend on the request of the other party". But he said NATO was a defensive alliance.
"NATO poses no threat to anyone. It is there for the purposes of mutual defence," he said at the news conference in Helsinki.
While there is no set time frame, here are the steps in NATO's membership process that would apply for Helsinki and Stockholm:
FINLAND AND SWEDEN SUBMIT MEMBERSHIP REQUEST
NATO officials and diplomats say that ideally the two countries should submit their requests together - most likely as letters sent to NATO headquarters - to simplify the bureaucratic procedure.
ALLIED GOVERNMENTS MEET
Representatives of the 30 allies meet in Brussels to discuss, and most probably accept, the membership request.
While many other aspirants, such as Ukraine and Georgia, have been asked to carry out reforms before a request can be accepted, Finland and Sweden are considered successful democracies with militaries that meet NATO standards.
MEMBERSHIP TALKS BEGIN; 'MARRIAGE VOWS' ARE MADE
This is likely to happen in Brussels at NATO headquarters, taking as little as one day for each country, assuming compliance with the terms of NATO's founding Washington Treaty.
The two countries are already considered to "contribute to the security of the North Atlantic area", as the treaty demands.
Known informally as NATO's "marriage vows", officials from Helsinki and Stockholm would be questioned as to whether they would uphold NATO's collective defence pledge that an attack on one ally is an attack on all.
They would also have to agree to pay their share of NATO budgets, take part in NATO defence planning and promise to respect rules on classified information.
NATO REPRESENTATIVES MEET AGAIN
The 30 allies would be likely to grant Finland and Sweden membership, giving them observer status at all allied meetings. However, they would still not be covered by NATO's collective defence guarantee.
All allied parliaments must ratify a membership approval by national governments. This can take anywhere between four months to a year, depending on elections, bureaucratic delays and summer recesses.
After the "deposition of the ratification" of all allies, both Finland and Sweden must also deposit their "instrument of accession" at the US Department of State, finally making both countries NATO allies.