Wilsher, who joined Fallon in 2000, will join Anomaly's New York office in the newly created role of president.
She will take responsibility for the day-to-day running of the agency, which has clients including Converse, Diesel and Umbro. Wilsher will take an undisclosed equity share in the business.
Her appointment comes just two months after Sony appointed Anomaly to the £50 million Sony Electronics account, following a shoot out against Fallon.
Anomaly secured the account through its recently opened London office, which is now the lead agency on the business.
Wilsher's departure follows that of Tony McTear, Fallon's creative director, who exited the agency last week as it announced ten redundancies.
The agency has no immediate plans to replace Wilsher but is understood to be considering both an internal promotion or an external appointment.