The bill is an important step for the government and Prime Minister Ulf Kristersson (M).
But Sweden's future as a member of the defense alliance remains in the hands of the countries that did not approve of Sweden, especially Turkey.
Thus, the resumed talks between Sweden, Finland and Turkey this week are an equally important piece of the puzzle in the continued NATO process.
In substance, the bill means that the Riksdag says yes to the 14 articles of the North Atlantic Treaty.
The most important, as you know, is article five, which means that Sweden has an obligation to see an armed attack on another member state as an attack on Sweden.
But that does not mean that Swedish armed forces are automatically sent to the attacked country.
It is a national decision to determine what support Sweden would send, and the decision will continue to require the approval of the Riksdag.
Hand in hand with Finland
The big change is instead about the government being given a mandate to make decisions about receiving military support from the defense alliance in the event of war, threat of war or to prevent violations of Swedish territory.
Already in existing legislation, the government can make such a decision regarding support from an EU or NATO country, but not from the organization NATO.
Going hand in hand with Finland has been a guiding light throughout the NATO process.
It was an important reason for the Social Democrats' rapid turnaround this spring, and it is a weighty reason why the bill is coming now.
From the beginning, the idea was that the respective parliaments would make the necessary parliamentary decisions only after all NATO countries had approved the two new members.
But just as little as the Swedish Social Democrats wanted the NATO issue in the election campaign, the people elected in Finland want it in theirs.
The fact that Turkey has signaled that they may approve Finland before Sweden also contributed to the fact that Finland wanted all the formalities completed as soon as possible.
And when Finland chose to reverse the process, the Swedish government did the same.
According to the plan, the Riksdag will vote on the bill on March 22 and it is hardly a wild guess that President Sauli Niinistö will sign the bill in connection with it, which is the last step in the Finnish process.
V and MP vote no
The government states in the bill that Swedish NATO membership would contribute to peace and security in the entire Euro-Atlantic region.
A similar conclusion was found in the security policy report that was drawn up by the eight parties in the Riksdag last spring.
But the Left Party and the Green Party do not subscribe to that analysis.
Their 42 members will vote no.
For the Social Democrats, the writing about nuclear weapons has been decisive and the wording was what was expected.
The government states that it sees "just as little as the other Nordic countries, that there are reasons to have nuclear weapons or permanent bases on Swedish territory in peacetime".
Today's bill should therefore be seen as a step on the way towards Swedish NATO membership.
When the Riksdag gives the green light, the government has the right to decide on Swedish accession to the NATO treaty and take the final step for Sweden to become a NATO member.