Kaspar Rorsted, who Adidas called the "perfect candidate", will take over on 1 October.
He is currently the boss of Henkel, whose brands include Persil detergent and Schwarzkopf shampoo.
He replaces Herbert Hainer, who has more than doubled revenue in 15 years in charge but has struggled to keep up with US rival Nike.
Adidas shares rose 5.4% to â‚¬88.52, while Henkel shares fell 3.4% to â‚¬77.88.
"The share price reaction speaks for itself," said Ingo Speich, an Adidas shareholder, told the Reuters news agency.
Mr Spiech, a fund manager at Union Investment, said he hoped the new boss would "end the long dry spell in the profitability of Adidas".
Adidas expects profits to have grown 10% in 2015, but its operating margin has been half that of Nike.
Mr Rorsted has worked at Oracle, Compaq and Hewlett Packard, as well as eight years running Henkel.
Shares in Adidas have risen more than 5% after the German sportswear firm named its new chief executive.