The recruitment process for a new chair began in October 2015 as Dame Judith Hackitt approached the end of her eight years in the role. She stepped down at the end of March and will begin her new post as chair of the manufacturers' organisation EEF on 4 April.
Brechin served as chief executive of NHS Fife for ten years before he retired on 31 March 2012. Between January 2014 and March 2015 he was interim chief executive of the State Hospitals board for Scotland.
The HSE said: "This is a short-term arrangement while the process to recruit a permanent successor continues."
The seven HSE board members are: Nick Baldwin, Jonathan Baume, Isobel Garner, Martyn Thomas, Sir Paul Kenny, Frances Outram, and Sarah Pinch.