It will open a 735 sq ft (70 sq m) boutique in the 100,000 sq ft (9,290 sq m) scheme in the city centre.
Princes Square was bought by Redevco in January. The landlord was represented jointly by Cushman & Wakefield and CWM.
There are 10 Vivienne Westwood stores in the UK – six of which are franchises – but this is the retailer’s first venture north of the border.
Vivienne Westwood (below) showcased her collection at London Fashion Week this year (left) after nine years’ absence from the show.