World number five Murray faces 27th seed Roberto Bautista Agut of Spain in a third-round tussle that, thanks to the arena's retractable roof, will be unaffected by the rain that is forecast.
In the first clash of this year's event between two former Wimbledon champions, five-times winner Williams meets Czech Petra Kvitova.
It will be the first time Williams has taken to the Centre Court in the singles since 2011, having crashed out in the first round in 2012 and missed the championships last year.
World number six Kvitova, who lifted the trophy here in 2011, has won her last two meetings with the American.
First up on Centre Court will be men's top seed Novak Djokovic, the 2011 champion, against Frenchman Gilles Simon.
The rain could be disruptive on the roofless Court One.
Women's second seed Li Na opens proceedings there against Czech Barbora Zahlavova Strycova before men's 11th seed Grigor Dimitrov of Bulgaria takes on Ukrainian Alexandr Dolgopolov.
(Editing by Tony Jimenez)
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