Jeakings, who is currently group finance director at Archant, will begin his new role on November 1.
He was previously group finance director of The Stationery Office, a provider of information management services to the Government and industry.
Before joining The Stationery Office he held a number of senior roles at Schlumberger, Graco and Dun & Bradstreet.
Fry, who has held the chief executive position at Archant since 2002, will leave on December 31. He starts his new role at Johnston Press on January 5 next year, replacing Tim Bowdler, who is retiring.
Jeakings said: "Archant has modest borrowings, a robust digital strategy, excellent brands, and a dedicated and dynamic team. Whilst these are challenging times for consumer media businesses, I believe we are well placed to make further progress when conditions improve."
Brian McCarthy will take over Jeakings previous role as Archant's group finance director on November 1.
McCarthy has been finance director of Archant Regional, the company's newspaper publishing division, since 2004.
Richard Jewson, chairman of Archant, said: "Archant is fortunate to have extremely able management, well capable of continuing to develop the business. Adrian is ideally placed and qualified to take on the role of chief executive.
"Both Adrian and Brian have contributed a great deal to our success and it is a tribute to John Fry that he has created such a strong management team."
Archant publishes around 80 regional magazine titles including Cotswold Life and Essex Life, as well as several regional newspapers, including the Evening Star, the East Anglian Daily Times and its flagship title the Eastern Daily Press.
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