Senator J.D. Vance drew a direct line on Wednesday from his traumatic upbringing in southwest Ohio to his new standing as the top lieutenant in Donald J. Trump’s conservative movement, promising the Republican National Convention that he would bring his working-class roots to Washington and help fight “for the people who built this country.”

Addressing the first national political convention he had ever attended, Mr. Vance, 39, accepted his party’s vice-presidential nomination — making him among the youngest Americans to ever fill that role — in an upbeat speech that was by far the most consequential of his fledgling yet rapidly ascendant political career.

Portraying himself as a child of Appalachia with a deep appreciation for the “grit in the American heartland,” Mr. Vance effectively framed his nomination as one for Mr. Trump’s white, working-class political base. He said he would be guided by the lessons learned from “Mamaw,” his deeply religious, foul-mouthed grandmother who raised him, and the memories of the friends and acquaintances from his old neighborhood who died of drug overdoses.

“I pledge to every American, no matter your party, I will give everything I have,” Mr. Vance said. “To serve you and to make this country a place where every dream you have for yourself, your family and your country will be possible once again.”

Sworn in to elected office for the first time just last year, Mr. Vance delivered a speech in Milwaukee that served as both an introduction to party delegates and a blueprint for his campaign to help return Mr. Trump to the White House. Mr. Vance will try to leverage his compelling biography to help reverse the former president’s losses in 2020 in the three battleground states with the highest percentage of white, working-class voters: Michigan, Pennsylvania and Wisconsin.

In his address, Mr. Vance mentioned Michigan six times, Pennsylvania five times and Wisconsin three times.