Verizon last week said that Armstrong was in talks to leave Oath.
Gowrappan, currently Oath's chief operating officer, will be taking the top job on Oct. 1, Verizon said.
Gowrappan joined Oath from Alibaba Group early this year.
Armstrong came to Verizon in 2015 following its takeover of AOL and headed Oath, which was created last year after the No.1 U.S. telecom company acquired the core business of Yahoo and merged it with AOL.
Oath owns more than 50 brands, including HuffPost, TechCrunch and Tumblr, but has failed to make an impact in the space occupied by Facebook Inc and Alphabet Inc Google.
(Reporting by Vibhuti Sharma in Bengaluru; Editing by Maju Samuel)