Murray, who joined the agency 11 years ago, will head up the newly created client-leadership team.
Today (6 July) the agency said it had created the client-leadership team to maintain "focused investment" in relationship with its clients, as it expands the business.
MPG said the new unit would work as a business partner with clients to produce "highly effective and creative solutions" and to ensure it delivered a high standard of service.
Paul Frampton, managing director of MPG Media Contacts, said: "We believe in collective success and working as one team with our clients.
"Natasha is the ideal candidate for this role, given her excellent client-service background and her immersion in all aspects of our business as managing partner.
"Her new role will ensure that we continue to deliver brilliant client service throughout the agency."
Murray was appointed managing partner in 2009 to work with clients including TUI Travel, BBC and Camelot.