The far-right leader signed the executive order at a ceremony on International Women's Day, two days before Congress was due to vote on overriding his veto.
Bolsonaro blocked the earlier legislation in October, arguing there was no funding to provide free menstrual supplies for more than five million low-income women and girls.
The new decree will be funded by a budget of 130 million reais ($26 million), according to the health ministry, but will reach fewer people -- an estimated 3.6 million.
"Menstrual poverty" is a major issue in Brazil, where women unable to afford tampons and pads often resort to scraps of cloth, diapers, bread or whatever else they can find when they get their periods.
A lack of menstrual supplies keeps one in four girls home from school each month, according to a 2021 report by a United Nations Foundation program called Girl Up.
Bolsonaro has been criticized for a history of remarks condemned as anti-women, including telling a congresswoman in 2014 she was "not worth raping" because she was "too ugly."
"When we speak of women, we must also speak of the family.... Respect above all, and the preservation of family values," he said at Tuesday's signing ceremony.
"You are beyond essential, you are indispensable for the future of this great nation. May you continue participating more and more with us in building it."
He added that if women decided, "we would have no wars in the world."
Bolsonaro is also due to speak Thursday at a privately organized event on promoting women's participation in politics.
However, it has been hit by backlash, as well, over the fact that all five speakers invited are men, including two of the president's ministers.
