SAN DIEGO (AP) — Parents held children born while they were stuck abroad. Long-separated couples kissed, and grandparents embraced grandchildren who had doubled in age.

The U.S. fully reopened to many vaccinated international travelers Monday, allowing families and friends to reunite for the first time since the coronavirus emerged and offering a boost to the travel industry decimated by the pandemic. The restrictions closed the U.S. to millions of people for 20 months.

Octavio Alvarez and his 14-year-old daughter zipped through a pedestrian crossing in San Diego in less than 15 minutes on the...