Datson, the former Tesco media director who has been covering the role of head of corporate comms for a year, is to step up to cover for the departing Alex Cole.
Cole is to leave in mid-July for private healthcare provider Bupa, which hired her as director of corporate affairs in March.
The search for her permanent replacement is being led by marketing director Sarah Warby.
Reilly, who will join on 1 July, was hired by Cole.
The former Freud Communications and Weber Shandwick executive has been with Open Road, which works for Sainsbury’s rival Asda, since 2010.
She was brought in to grow the public affairs agency’s corporate client base and has led its work for Coca-Cola, among other clients.
Open Road was acquired by Sainsbury’s corporate PR agency Blue Rubicon in February this year and Reilly, along with her three fellow Open Road directors, was made a director of Blue Rubicon.
Reilly said: "I'm really excited to be joining Sainsbury's at such a fascinating time for the business and for the retail sector as a whole."