Wright, currently the agency's deputy managing director, will replace Matt James who resigned from the role last month.
The agency did not consider external candidates for the post, opting instead for Wright, who has been with Manning Gottlieb OMD for three years.
James continues to work his notice period at the agency, but in a different role.
Wright joined Manning Gottlieb in 1999 as a partner and was promoted to deputy managing director last year. Before this she had ten years' experience at creative agencies, latterly as a partner at HHCL & Partners.
Nick Manning, the chief executive of Manning Gottlieb, said: "There was no issue of outside candidates. We have a well-balanced board and Alison was the logical and natural candidate."
Manning Gottlieb has also changed the responsibilities of two of its nine board members. Andrew Stephens becomes the marketing and new-business director, while John McGeogh, the agency's broadcast director, becomes the buying director.
Wright said: "The role will be a bit different. The serious advantage of not being a media specialist is that things are changing incredibly quickly and it's important to identify areas of additional services that are growing fast."