Shop Direct, which owns Littlewoods and the online guise of Woolworths, said Baldock will join in September when incumbent Mark Newton-Jones retires after nine years.
Baldock, 41, has a financial rather than retail background, having worked for Barclays, Bain & Company and Ernst & Young.
Baldock has most recently worked as a managing director at Lombard, which offers financing to smaller companies.
The Oxford graduate also has a degree from Harvard.
Newton-Jones said in January that he hoped to “pursue new challenges in the medium term” as he left the retailer.
Shop Direct, owned by the Barclay brothers, also runs online clothes companies Very and Isme.