The troops have been on standby since January, before Kosovo's ethnic Albanian majority declared independence from Serbia on February 17.
The declaration of independence was backed by the the United States and many European nations, but was rejected by Serbia and its ally Russia.
Browne said that since then the security situation had been tense with sporadic incidents of violence.
The UK battalion will supplement about 16,000 Nato-led peacekeepers which are already in Kosovo.
Britain is responsible for providing Nato's standby reserve force for the Balkans for the first six months of this year.
Nato has had peacekeepers in Kosovo since the end of the 1998-99 war between Serbian forces and ethnic Albanian separatists.