Mr Larsson will report to the designer who will continue to oversee the company`s creative look and strategy.
Analysts say luxury brands are increasingly hiring from mass-market firms.
The iconic company has been struggling to boost profits as a stronger dollar reduces the value of sales from outside the US.
Mr Larsson is credited with reviving sales at Old Navy, where he offered the latest styles at low prices.
Annual sales under Mr Larsson`s leadership rose 8% in 2014 and became Gap`s biggest business.
`Natural progression`
Mr Lauren, who will turn 76 in October, said Mr Larsson would be in charge of growing future sales.
Speaking of his replacement, Mr Lauren said: "He understands what dreams are. In this business, it`s about dreams because you are dreaming ahead and you`re about progress and change and newness."
The announcement caused Ralph Lauren`s shares to rise 3.9% in post-trading hours.
Odeon Capital analyst Rick Snyder said the change in chief executive was "positive" and "just a natural progression."
He thinks Mr Larsson`s background will help the Ralph Lauren brand to reorganise and create greater efficiencies in their supply chain.
Lauren`s fashion empire includes some 25 brands including Polo, Club Monaco and Denim & Supply. The company makes clothing, accessories, furniture, home decor items and footwear under its labels.
Mr Larsson, 41, led Old Navy from 2012 and has been credited with boosting sales, even as other Gap labels faltered. Before taking over Old Navy, he worked for the Swedish brand H&M for 15 years.
Ralph Lauren made $7.5bn (£5bn) in sales last year.
Mr Lauren said his successor was "exceptionally talented" and would bring "a fresh and exciting global perspective" to the company.
More about:
