Viala, a French national, will officially take over at the UK business in the summer after a phased handover of her present job.
Sow, who held the post of chairman and chief executive at Bouygues UK for eight years, left at the start of February.
His departure prompted an immediate boardroom reshuffle with Lionel Christolomme, former UK construction managing director, immediately stepping up to take over the £800m turnover UK business as chief executive.
Viala joined the Bouygues group in 1987 and was appointed CEO of Bouygues Energies & Services (France: Western regions) in 2015.
Until Viala takes up the post, Olivier-Marie Racine, deputy CEO of the global Bouygues Construction business, is acting as chairman of UK operations.
A spokeswoman for Bouygues UK said: “The proposal of Fabienne Viala as Bouygues UK Chairman will be put to the Bouygues UK Board of Directors later this year.
“Over the coming months, Fabienne Viala will gradually hand over her current responsibilities as CEO of Bouygues Energies & Services (France: Western regions).
“This will allow her to start working with the UK team and officially take up her duties as Bouygues UK Chairman by the summer of 2016.”