Hargreaves started up Credo in 2003, after quitting Firefly Communications, where he was deputy MD.
Hargreaves takes over as UK MD of the Next Fifteen-owned agency from Barry Legetter.
Hargreaves and Credo's three other staff including co-founder Nick Rappolt, ex-Herald Communications MD Stephanie McLeod and consultant Rob Taylor will transfer to Bite on 3 January. The Credo name will be scrapped.
Leggetter has been covering the MD role since 2004, when Sheryl Seitz made way for him as part of a restructure of the agency's management (PRWeek 17 September 2004). He will continue in his position as Bite group chairman.
Seitz joined Apple earlier this year (PRWeek, 22 July 2005).
The value and structure of the deal has not been disclosed. In the year to 31 March 2005, Credo's fee income was £254,000 on sales of £311,000.
Hargreaves left Firefly following a failed boardroom coup, which led to him and three of Firefly's six other directors quitting.
Credo's clients include FTSE 100 accountancy software maker Sage, Barclays' small business subsidiary, ClearlyBusiness and BBC Worldwide.
But the acquisition could prove more difficult for security firm Check Point Software Technologies, which appointed Credo to handle its pan-European PR following a fallout with Firefly over fees (PRWeek 23 September).
Bite's recent win of the account for Check Point's much larger rival Symantec could present a conflict of interest.