She will leave in April to set up Godmother, a consultancy working with start-up organisations.
IPG Media Brands, the media division of Interpublic Group, will replace her at Initiative.
Weavers has worked in agencies for more than 25 years. She worked at J Walter Thompson, WCRS and Vizeum, before joining UM, Initiative’s sister agency, in 2011.
She is well regarded in the media industry and was a judge for Sales Team of the Year at the 2016 Media Week Awards.
Weavers said: "Having experienced the rollercoaster of agency life for over 25 years I know what is needed to turn businesses around and establish new ones.
"With that knowledge, and the support of others, it feels like a great time to start an incubator company – hence the birth of Godmother. I’m really looking forward to working with the brightest and the best in the future."
IPG Media Brands suffered a blow in the UK in 2015 when Initiative lost Tesco’s £90m media account to WPP’s MediaCom.
Initiative has been in recovery mode since then, winning nine accounts and working on campaigns such as #ContiQuiz for Continental Tyres’ Euro 2016 sponsorship and 'Amazon Sponsors Downton Abbey' for Amazon on ITV.
Caroline Foster Kenny started as chief executive of IPG Media Brands, EMEA this week, filling a leadership gap since Andy Jones departed in spring 2016 as UK & Ireland chief executive.
A spokesman for IPG Media Brands said: "We've loved having Sally with us over the last six years and we wish her the best of luck with her new venture."