The industry veteran, who took over from Sir Frank Chapman as the group’s boss in January 2013, has quit for “personal reasons”, BG said.
Finlayson was one of three internal candidates shortlisted to replace Chapman after his planned retirement, but BG said it would be seeking an external successor.
Until a permanent replacement is appointed, BG chairman Andrew Gould will become interim executive chairman.
Gould said: “The board of directors is fully committed to the group’s strategy, which is built upon a portfolio of high-quality assets. The company must accelerate the creation and delivery of the longer-term value for our shareholders, while delivering the group’s business plans.
“The board felt that it was in the best interests of the group to accept Chris’ resignation and seek fresh leadership to deliver both of these priorities.”