More tough negotiation and reforms lie ahead if it is ever to join the EU. Its neighbour Croatia joined in 2013.
Bosnia's move comes more than two decades after it emerged from a three-year conflict that cost about 100,000 lives, when Yugoslavia fragmented.
The EU foreign policy chief saw the bid as a step towards European unity.
"At a time when the union is questioned from within, seeing that with our immediate neighbours there is such an energy and willingness to join and work hard to adapt their countries, society, economy, institutions, systems to the European standards, gives us the sense of responsibility we have also towards our European Union citizenship," Federica Mogherini told journalists.
Integration with Europe is seen as a way to help Bosnia's ailing economy and overcome its reputation for corruption that scares off investors.
Last March, EU foreign ministers and Bosnia signed a Stabilisation and Association Agreement that had been on hold since 2008, paving the way for the application.
Dragan Covic, the chairman of Bosnia's tripartite presidency, said there would be "years of many challenges ahead", the AFP news agency reports.
He submitted the application to Dutch Foreign Minister Bert Koenders, whose country currently holds the six-month EU rotating presidency.
The EU was happy to see "Bosnia back on the reform path", AFP quoted Mr Koenders as saying.
Bosnia-Herzegovina has formally applied to join the 28-nation European Union - a milestone in its efforts to overcome political and ethnic divisions.