It comes amid a broader management transition which, as previously announced, sees chief executive Bob Dudley step down to be replaced by the group’s upstream chief Bernard Looney (who takes up the CEO role in February).
Gilvary has been at BP for 34 years of which eight were spent as CFO.
His replacement Auchincloss has worked in BP Upstream alongside Looney as the division’s CFO.
Auchincloss takes up the group CFO role in July and in the meantime he will work alongside Gilvary to ensure an orderly handover.
"All of us at BP will greatly miss Brian's clarity of thought, his candour and his commitment to the company. I appreciate that he has agreed to stay in post until mid-year to ensure a successful handover to Murray,” Looney said in a statement.
“I have worked side-by-side with Murray for many years and have the utmost confidence in his ability to step into this critical role."
Chairman Helge Lund added: "We will miss Brian's financial stewardship and strategic insights. He is one of the architects of today's BP, key to its transformation into a safer, simpler and stronger company.
“After a thorough selection process, the board is pleased to have chosen Murray as BP's next CFO. With his international financial and commercial experience and a deep understanding of the whole group, he will play an important role as BP continues to develop in a fast-changing energy market.”