Nickolds has been with the business since 1994, when she joined as a graduate trainee at the retailer’s Oxford Street flagship store. She joined the board in 2013, as buying and brand director, before moving to her current role last year.
Nickolds will take up the post in January; until then, the business will be led by operations director Dino Rocos.
Sir Charlie Mayfield, chairman of the John Lewis Partnership, said: "At a time of transformation in the retail sector, Paula's progressive and dynamic leadership is just what's needed for the next phase of modern retailing."
Street stood down as managing director in September with immediate effect, after he was chosen by the Conservative Party candidate to be the inaugural West Midlands mayor at next year’s election.
Nickolds said: "Driven by our unique business model, and with innovation in our DNA, I am immensely excited to lead John Lewis on the next stage of our journey."