If accepted, it will become the 29th member state in the union, which the country hopes will boost its economic and political standing.
The country, which has a tumultuous history of conflict during its time as part of the former Yugoslavia, undertook an ambitious package of reforms last year as part of an EU initiative to inject momentum into its eventual EU membership.
The reform agenda addresses its economy, jobs, social welfare, pensions, public administration and governance.
Dutch foreign minister Bert Koenders received the application on behalf of the EU member states, as his country currently holds the six-month EU rotating presidency.
“While commending the encouraging start made in implementing an ambitious reform agenda, Minister Koenders urged the Bosnia and Herzegovina authorities to maintain positive momentum by continuing to implement the necessary reforms, engage with civil society and consolidate progress,” said the official EU statement.
“The Council Conclusions of December 2015 reinforce Bosnia and Herzegovina’s EU perspective and outline that meaningful progress in the implementation of the reform agenda is necessary for the EU to consider a membership application from Bosnia and Herzegovina.
“Progress on the adaptation of the stabilisation and association agreement following the accession of Croatia and a functioning coordination mechanism on EU matters are important for Bosnia and Herzegovina’s progress towards EU accession.”
Neighbouring Croatia joined in 2013.
The EU said its General Affairs Council will decide on Bosnia and Herzegovina’s EU membership application in due course, depending on its progress in implementing the reform agenda.
The UK's Foreign Secretary Philip Hammond said last July that Bosnia and Herzegovina's reform agenda was “a landmark step” that “will help to stabilise the economy and encourage much-needed economic development, allowing Bosnia and Herzegovina to advance on its chosen path towards membership of the EU”.