Mr. Ossoff, then, is a big get: Beyond Ms. Abrams, there are few Democrats in Georgia with as much name recognition and proven fund-raising power. He raised more than $23 million for his 2017 special election campaign — at the time, the most expensive House race in history — and drew national attention for being competitive in a district, Georgia’s Sixth, that had not elected a Democrat since 1976.

He came close to winning outright in the first round of voting, but lost a runoff to a Republican, Karen Handel, by about four percentage points. (Ms. Handel lost re-election to another Democrat, Lucy McBath, in 2018.) It was a devastating loss for Democrats, but also a remarkable achievement in the Sixth District, which the former House speaker Newt Gingrich held for 20 years and Republicans normally won by double digits.

Before taking charge of a documentary film company, Mr. Ossoff, 32 — if he won, he would be the youngest sitting member of the Senate by a large margin, behind 39-year-old Josh Hawley, Republican of Missouri — spent five years working for Representative Hank Johnson, an Atlanta Democrat.

Three other Democrats are already running for Mr. Perdue’s seat: Mayor Ted Terry of Clarkston; former Mayor Teresa Tomlinson of Columbus; and Sarah Riggs Amico, who ran for lieutenant governor last year on Ms. Abrams’s ticket.