Barnett will take up the role as chairman of the SG Kleinwort Hambros Bank on 6 November, the date the legal merger between Societe Generale and the Kleinwort Benson bank is due to complete.
Newbury will remain in post until the same date before becoming chairman of the board at investment office Sandaire.
The board moves follow Societe Generale’s acquisition of Kleinwort Benson in June 2016, with the private banking business merged with SG’s Private Banking Hambros brand.
The merger created a firm with £16bn of client assets.
Prior to joining Kleinwort Benson in 2014, Barnett was a senior partner at Deloitte Financial Services Practice and specialises in private banking and wealth management.
In a statement, the company said: “In his new role Barnett will work closely with the SG Kleinwort Hambros Bank Board, and will act as a direct liaison between the Board and Eric Barnett, Chief Executive Officer of Kleinwort Hambros, to build on the strengths of Kleinwort Hambros in the UK, Channel Islands and Gibraltar.”