The vote in the Congress Chamber on Thursday saw 65 yes votes and 33 votes against.
The bill now has to pass the House of Representatives before it can be signed into law by President Joe Biden.
It is the first federal tightening of US gun laws in almost 30 years.
Among other things, the text provides for extended background checks on gun buyers under the age of 21.
In addition, financial incentives are to be created for the individual states to temporarily remove the guns from potentially dangerous gun owners.
Billions are also planned for safety in schools and better psychiatric care in the country.
The Democrats would have liked to take further measures.
They encountered resistance from the opposition Republicans, who have a blocking minority in the Senate.
In view of the political polarization in the USA, the fact that both parties were able to agree on a legal text on gun law is already a success.
Political pressure after massacres in Uvalde and New York
Two serious attacks in May sparked renewed debate in the United States about tightening gun laws.
First, in the state of New York, an 18-year-old shot dead ten people in front of and in a supermarket with an assault rifle, apparently for racist reasons.
At an elementary school in the small Texas town of Uvalde, an 18-year-old killed 19 children and two teachers.