This was published under the 2010 to 2015 Conservative and Liberal Democrat coalition government
A Memorandum of Understanding - signed by Mr Brokenshire and Bolivian foreign minister David Choquehuanca - will see more expertise sharing on aspects of drug trafficking.
This includes work to tackle money and assets laundering.
Bolivia is thought to be the world’s third largest cocaine producer.
Menace of narcotics
Mr Brokenshire said: ‘The UK and Bolivia already have a strong working relationship. It’s clear that by working together we are best placed to protect our citizens from the menace of illegal narcotics.
‘This Memorandum of Understanding will deepen our ties across a range of areas and I look forward to seeing positive results flow from it.’
The UK’s Serious Organised Crime Agency and the Bolivian Anti-Narcotics Force already exchange information about criminal organisations.
Meanwhile, a UK-donated drugs-testing laboratory in Bolivia is now fully functioning and is used to test samples from seizures.