At BBH, she will report to John O'Keeffe, executive creative director. She leaves glue this week and will join BBH on March 6 as head of digital production.
Glue has not yet found a replacement for Stanhope, who has been with the agency for three years.
The appointment comes shortly after BBH picked up a digital brief from Unilever to be the lead creative and strategic digital agency for Lynx/Axe.
It is the first piece of digital business that the agency has picked up after a pitch solely against specialist agencies.
O'Keeffe said: "Michelle brings a wealth of expertise in getting great ideas out across multiple platforms. We're delighted she's chosen to join us at such an exciting time for BBH and our industry."