Foreign Minister Ann Linde (S) and her Finnish counterpart Pekka Haavisto are in Brussels, where they are expected to hold a press conference with NATO Secretary General Jens Stoltenberg at lunchtime on Tuesday.
Before that, the ambassadors of the 30 NATO countries must have signed the Swedish and Finnish accession protocols, which now gives the two countries the status of "prospective members" - invitees, in NATO English.
This paves the way for the ratification process in which all NATO countries must approve accession also at home, in the various parliaments.
Only when this has been done, and the accession protocol has been archived in the right place in Washington, will Sweden and Finland become full members of the military alliance.
Several countries, not least in the Nordic and Baltic countries, are expected to compete to be the first to ratify the new memberships.
Turkey wants to see concrete consequences
At the same time, the question remains as to what Turkey will do - despite the agreement reached at the NATO summit in Madrid last week, when Turkey lifted its veto on starting the membership process.
However, Turkey has clearly stated that it wants to see concrete consequences from the wording on the fight against terrorism, arms exports and extradition that the countries agreed on in Madrid.
They must follow this document.
If they do not, we will not take them into NATO, says Turkish Foreign Minister Mevlut Cavusoglu in an interview with the Turkish television channel NTV, according to the English-language government agency Daily Sabah.
The Turkish parliament must also approve the membership of Sweden and Finland.