Fall on someone's neck

[W]hen Theseus saw him, his heart leapt into his mouth, and he longed to fall on his neck and welcome him.

If he expected either of them to fall on his neck and weep tears of gratitude at his pompous announcement, the colonel was disappointed.

I ought to fall on your neck with joy. . . . You are my father's friend, my mother's, mine.

"[T]he moment your delinquent showed the slightest sign of decency . . . you fell on his neck as if he had rescued you from drowning."

[A]fter falling on my neck and hugging me and calling me “cousin” like a character from a Jane Austen novel, . . . she sat me down.