Mr Stubb, a former prime minister, said he wants to "see Finland in the core of Nato" as it contends with an unpredictable Russia on its border.
"We are a security provider, not a security consumer," he said. "We have no limits to our Nato membership. We have one of the strongest defences in Europe and we are a security asset in Nato.
"We want to be in the core of decision-making, sit around the tables where decisions are made."
With Nato's future in doubt as Donald Trump lurks in the wings, Mr Stubb told Finns to stay calm after the US Republican front-runner suggested he might not protect allies from a Russian attack.
"US election campaigns are very different from Finnish elections and the rhetoric used is quite a lot stronger," he said.
As if underlining that difference, the two candidates spoke jointly to the press as results came through. Mr Stubb told his defeated rival Pekka Haavisto "you are one of the finest people I have ever met".
Mr Stubb took 51.6 per cent of the vote to Mr Haavisto's 48.4 per cent in the second-round run-off to succeed Sauli Niinisto.
While Prime Minister Petteri Orpo oversees domestic policy, Finland's president is an influential voice in foreign and security matters.
Finland had long sought cordial relations with Moscow but, like its neighbour Sweden, was spooked into a rethink by Russia's assault on Ukraine.
While Finland and Russia co-operate on practical issues such as guarding their 1,340-kilometre border, there is "no political relationship" with the Kremlin, Mr Stubb said. Finland last year closed the eastern land border after a rush of migrants entering from Russia.
"Before Russia ends its war of aggression against Ukraine, it will be very difficult to have a relationship with Russia," he said.
Finland was admitted to Nato last year after addressing Turkish grievances about Kurdish militants on its territory. Sweden is still waiting for the nod from Hungary.
In one campaign disagreement, Mr Stubb had signalled he was open to nuclear weapons being stationed on Finnish territory, while Mr Haavisto was opposed.
The nuclear arsenal controlled by the US, as well as those of Britain and France, are regarded as the ultimate guarantor of Nato's security.
However, Mr Trump's return to the fray has cast doubt on whether the US would honour the mutual defence guarantee in Nato's founding treaty.
Estonia's Prime Minister Kaja Kallas said Mr Trump's comments should be a wake-up call for allies to spend more on defence. The Biden administration has pledged its support to Finland and Nato.
"I think at this stage it is best to remain calm and focus on building our Nato membership," Mr Stubb said.