Jacinda Ardern's mother imagines the first family will be looking forward to getting home.

The Prime Minister, her partner Clarke and their new baby girl are due to leave Auckland City Hospital around 11am this morning.

There's no word on the little girls name yet, but her grandmother Laurell Ardern says she's a little cute.

She described the first baby as having dark hair, dark eyes and fine features.

Mrs Arden says Clarke and Jacinda will be wonderful parents.

"Jacinda's the Prime Minister, she'll work things out for herself."

The first family are due head home around 11am.