Australia's reelected Prime Minister Scott Morrison has named his Cabinet that includes the first indigenous Australian.

Morrison named Ken Wyatt as the indigenous affairs minister on Sunday, a week after his conservative coalition won a surprise victory.

He also announced Marise Payne will be the women's minister as well as the foreign minister, the position she held in his previous government.

She is one of a record seven women in the Cabinet.

Josh Frydenberg and Mathias Cormann will stay in their posts of the treasurer and the finance minister, respectively.