Amazon.com Inc. in the coming weeks is set to roll out new lines of private-label brands that will include its first broad push into perishable foods, according to people familiar with the matter.

The new brands with names like Happy Belly, Wickedly Prime and Mama Bear will include nuts, spices, tea, coffee, baby food and vitamins, as well as household items such as diapers and laundry detergents, these people said.

The...