Formerly chief operating officer, Brown, who takes over from July 16, replaced Professor Steve Edwards, who has acted as interim chief executive since March.
Brown will be personally responsible to Defra ministers and to ministers in Scotland and Wales for the delivery of Animal Health's annual performance targets, and to Parliament for ensuring propriety in management of public funds.
A Defra statment said: "[Brown] will lead Animal Health through significant organisational changes, including implementing the Agency's Business Reform Programme, which will begin to modernise Animal Health's operating model.
"During this time, Animal Health will participate in the debate on cost and responsibility sharing and on developing animal health and welfare policies in England, Scotland and Wales.
"Animal Health will also continue to deliver an effective response to outbreaks of exotic and endemic animal disease in order to protect public health and deliver a successful and sustainable livestock industry."