Brown joined the Aberdeen-based firm in 2010 and is responsible for its legal, compliance and company secretarial functions.
He was previously a corporate partner at law firm Maclay Murray & Spens, advising on international mergers and acquisitions and joint ventures, and served as European vice-chair of cross-border transactions for Lex Mundi.
Brown read law at Pembroke College, Cambridge, and practiced with Freshfields in London and Arthur Robinson & Hedderwicks in Melbourne before returning to Scotland in 2000.
Wood Group, which earlier this month announced that chief executive Bob Keiller will also be leaving at the end of the year, said: “The board would like to thank Robbie for his contribution to the success of the group as a member of the group executive since 2010 and wish him well in the future.
“A process to identify successors for Robbie’s roles is underway and a separate announcement will be made in due course.”