The married millennial parents are coming—after years of putting off marriage or having children or both.

The trend among young parents, who are primarily the generation known as millennials, will be toward a growing majority of children born inside marriages, according to a new forecast from Demographic Intelligence, a research firm that forecasts marriage and birth trends.

Demographic Intelligence predicts that ultimately about 60% of the children of millennials will be born to married parents, up from about 45% today.

“The narrative about millennials has been they’re putting parenthood before marriage, never going to get married,” said Sam Sturgeon, president of Demographic Intelligence, based in Charlottesville, Va. “Now that the cohort is in the middle of their 20s, from here on out you’re going to see a lot of millennial marriages and a lot of millennial married births.”

Millennials, defined in Mr. Sturgeon’s forecast as those born between 1980 and 2000, are the largest and most diverse generation in U.S. history. Earlier this year, they became the largest generation in the U.S. labor force, surpassing Generation X, those ages 35 to 50, according to the Pew Research Center.