Goh, who joined the oil and gas major as a director in 2014, succeeds Gerard Kleisterlee in the deputy chair role and as a senior independent director.
Shell said Kleisterlee, who joined the company nine years ago, will not seek a re-election at its annual general meeting.
The company also said Neil Carson will take over from Kleisterlee as chair of the remuneration committee.
Goh, a Singaporean national, is also the chair of SATS Ltd, and was chief executive officer of Standard Chartered Bank, Singapore, from 2001 until 2006.
(Reporting by Samantha Machado and Pushkala Aripaka in Bengaluru; Editing by Maju Samuel)
