It also came as US President Joe Biden set out tough new nationwide rules designed to stanch the flood of new infections, ordering companies with 100 or more personnel to ensure all of them are vaccinated, and requiring that all federal employees and contractors also get the shots.
Around 600,000 students attend a public school managed by LAUSD, about 220,000 of whom are eligible for a vaccine.
The passage of the motion at Thursday's meeting could set a precedent for school boards across the country.
Kelly Gonez, LAUSD board president, welcomed the vote: "The vaccine is safe, effective, & the best way to keep our students protected against the virus," she tweeted after the meeting.
"We will work to ensure families have reliable medical information in the coming weeks."
The district already mandates regular testing for children, and masks are required on campus, both indoors and out. Staff must be vaccinated.
Under the new rules, all children attending in-person classes will need to have their first dose by November 21. They must have had their second dose in time for full immunity by January 10.
Scientists say the second jab confers maximum immunity two weeks after being administered.
A child who turns 12 during the school year will have 30 days to get their first shot.
The plan has the support of teachers' unions and many parents, but -- as elsewhere in the United States -- a significant and vocal minority is strongly opposed to vaccines, despite overwhelming scientific evidence that they are safe and effective.
Local health officials say around 58 percent of those aged between 12 and 18 have had at least one shot.
The LAUSD meeting heard from a number of parents who expressed concerns about the vaccines, and insisted it was their right to choose if their child was inoculated.
But it also heard from doctors who repeated the scientific establishment's refrain that the shots have been rigorously tested and found to be both safe and highly effective.
Some contributors drew parallels with previous battles against diseases like polio, which has been largely wiped out worldwide by vaccination programs.
Schoolchildren in many parts of the United States are already required to be vaccinated against a raft of communicable diseases, including diphtheria, hepatitis B and measles.
Vaccines, masks and other mitigation measures against Covid-19 have become deeply political issues in the United States.
Politicians in mainly Republican-led states and counties have cited personal freedom as a reason to resist imposing rules that doctors say would protect their populations.
A free and widely available vaccine program in the United States is credited with taming earlier surges in the coronavirus, a disease that has claimed more than 650,000 lives and sickened millions more in the country.
But Delta's emergence has threatened to reverse progress, and case numbers have risen nationwide in recent months, concentrated in places where vaccine take-up is low.
