Gillingwater will succeed current chairman Lord Smith of Kelvin when he stands down from the board on 1 January 2016 after 13 years.
As deputy chairman Gillingwater will continue with his existing roles as senior independent director and chair of the remuneration committee, SSE said.
He joined the board of SSE as a non-executive director in 2007 and became senior independent director in 2012. He is also the current chairman of Henderson Group and has served as the chairman at both European investment banking at Credit Suisse First Boston, and at the shareholder executive in the past.
“I am delighted that Richard will become deputy chairman and, in due course, chairman of SSE. He will bring to both roles extensive knowledge of the sector, experience of dealing with business issues in a FTSE 100 company and in addressing the needs of all of SSE’s stakeholders, from customers to investors,” Smith said.
Smith joined the board of SSE in 2003 as a non-executive director and became chairman in 2005.
Gillingwater added: “I am looking forward to supporting him in the months ahead as we work together to ensure that SSE continues to fulfil its core purpose, of providing the energy people need in a reliable and sustainable way.”