The 39-year-old leaves the Pilgrims - who are three points above the Potters in the second tier - to replace Alex Neil on a three-and-a-half-year deal.
Schumacher spent two years in charge at Argyle, leading them to the League One title with 101 points last season.
Stoke, without a win in eight, are three points above the drop zone and on to their sixth manager in six years.
Neil was sacked on 10 December after 16 months in charge, having led the club to a 16th-placed finish in 2022-23.
Schumacher follows the same route as Tony Pulis, Stoke's most successful manager of the past 50 years, who left Home Park to return to the Potteries for a second spell in charge in 2006, culminating to the club's return to the top flight in 2008.