Canada, for example, says that it expects to ratify their accession protocol in just a few days.
Stoltenberg said that Nato allies "are determined to work through all issues and reach rapid conclusions."
"All allies agree on the importance of Nato enlargement. We all agree that we must stand together, and we all agree that this is an historic moment which we must seize," he told reporters, at Nato headquarters in Brussels.
Public opinion in Finland and Sweden has shifted massively in favour of membership since Russia invaded Ukraine on February 24.
Finland and Sweden co-operate closely with Nato. They have functioning democracies, well-funded armed forces and contribute to the alliance's military operations and air policing. Any obstacles they face will merely be of a technical, or possibly political nature.
Nato's membership process is not formalised, and the steps can vary. But first their requests to join will be examined in a sitting of the North Atlantic Council (NAC) of the 30 member countries, probably at ambassadorial level.
The NAC will decide whether to move toward membership and what steps must be taken to achieve it. This mostly depends on how well aligned the candidate countries are with Nato political, military and legal standards, and whether they contribute to security in the North Atlantic area. This should pose no substantial problem for Finland and Sweden.