Rogers took over the running of Argos in 2016 shortly after J Sainsbury PLC (LON:SBRY) bought the electricals and housewares chain having served as the supermarket's chief financial officer from 2010 to 2016.
Rogers will leave on 31 October and join WPP in early 2020, succeeding Paul Richardson when he retires as group finance director.
He said that the opportunity to join “a technology-driven business with creativity at its heart” was “impossible to resist”.
WPP chief executive Mark Read added: "John is not only an accomplished CFO, but also a leader with extensive experience of business transformation.
“His priority will be to lead a finance function that best fosters investment in creativity, technology and talent in support of WPP's new strategy for growth."
Rogers will be paid an annual salary of £740,000 in the new role.
Meanwhile, Argos's retail and logistics teams will now report into Simon Roberts, retail and operations director, and Argos's commercial team will report into Paul Mills-Hicks, commercial director.
Analysts at AJ Bell hinted that the loss of a highly-experienced, highly-rated "obvious internal replacement" for current CEO Mike Coupe may "suggest that the latter is staying put for some time" despite the damage his reputation suffered from the recent failed merger with Asda.
Investment group Shore Capital went further, calling Rogers' departure "the clearest smoke signal yet that Mr Coupe is going nowhere".
Shore Capital said that Rogers is "a great appointment for WPP", but a "demonstrable loss to the Sainsbury senior management pool" which may do little to sweeten the supermarket group's share prices.
“While Rogers’ retail experience might not make him an obvious fit for WPP at first glance, he will be familiar and have relationships with the companies behind the consumer brands in the company’s client base, " noted Broker AJ Bell.
WPP has had a tough time in recent years with shares sliding 50% between 2017 to 2019 and the first half of this year saw the multinational’s profits drop by 44%.
--Editd to add comments from AJ Bell and Shore Capital