The division, launched in 1998, specialises in programmes designed to break down barriers to employment for the long-term unemployed.
Edelman won the account following a four-way pitch.
Campaign Communications and Maggie Wright Associates worked on the account previously.
The brief includes stakeholder-relationship building and media relations to raise awareness of Reed in Partnership.
Associate director Iain Twine will lead the account, working closely with MD public affairs Alex Bigg.
Both will report to head of corporate communications Alan Davidson.