Tritton joined Target in 2016 and is currently its chief merchandising officer. He takes over his new role at the houseware retailer in November, Bed Bath & Beyond said in a statement.
At Target, he was responsible for store revamps, private-label brands, product sourcing and design.
Tritton, who has 30 years of experience in the industry, also played a major role in doubling sales of department store chain Nordstrom Inc's private label business.
His appointment comes at a time when Bed Bath & Beyond is struggling to keep pace in a rapidly changing retail landscape, dominated by the popularity of online shopping.
Earlier this year, a group of activist investors had piled pressure on Bed Bath & Beyond, citing falling sales under Temares' leadership. Its sales have fallen in eight out of the past 14 quarters.
Since then, the company has cut jobs and eliminated key executive roles in its attempts to reduce costs.
Chris Kiper, managing director at Legion Partners Asset Management and one of the activist investors that pushed for a change at the company, cheered the appointment.
"We are so excited that he is joining (Bed Bath & Beyond)," Kiper said.
Tritton's focus at Bed Bath & Beyond will be to enhance store and online experience and improve its product offerings, the company said.
"While it remains to be seen if he is the right person for the job, the merchandise improvements at Target during his tenure have been impressive, particularly the repositioning within home and apparel," Gordon Haskett analyst Chuck Grom said.
Separately, Target named company veteran Michael Fiddelke chief financial officer and said two executives would assume interim leadership of the retailer's merchandising organization, which comes months ahead of the crucial holiday shopping season.
(Reporting by Nivedita Balu in Bengaluru; Editing by Anil D'Silva)
By Nivedita Balu