WPP brought the legal action claiming that Murphy, David Golding and Ben Priest, the founding partners of Adam & Eve, were in breach of contract when they set up the agency.
It alleged they approached staff and clients of their former agency, RKCR/Y&R, while still bound by the terms of their gardening leave.
The case was due to be heard at London's High Court next week.
Full statement by Adam & Eve:
"This statement is made by James Murphy, David Golding and Ben Priest on behalf of Adam & Eve, following settlement of the proceedings commenced by Young & Rubicam against Adam & Eve in the High Court in London.
"The terms of settlement are confidential, but this statement is given to apologise unreservedly since we realise that despite assurances given in June 2007, we over-stepped the mark when setting up our new agency and dealing with clients whilst still under the contractual obligations of our gardening leave.
"We also retained proprietary information belonging to Y&R albeit unintentionally.
"We acknowledge that WPP and Y&R are entitled to protect their business interests.
"With this settlement and apology we look forward to putting this matter behind us."