The money will be used to build new reception centres and provide other services including "food and accommodation, access to water sanitation and hygiene" to the roughly 7,400 migrants currently based in the Balkan state, the EU delegation said in a statement.
Since 2018 Bosnia has become a key transit country on a route funnelling migrants west to the border with EU member state Croatia.
The migrants, some 36,000 of whom have entered Bosnia in that time, hail mainly from countries in the Middle East, Asia and North Africa.
While most eventually manage to continue their journey westward, pushbacks by Croatian police are common, leaving many marooned in Bosnia for long periods.
Poor and paralysed by a fractured government, Bosnia has struggled to provide adequate support.
The construction of new reception centres is a contentious political issue in the Balkan state, where the influx of migrants has caused tensions with some local communities.
The largest centres are currently based in the northwest, in the towns of Bihac and Velika Kladusa.
Bosnia's Serb-run half, meanwhile, refuses to build any reception centres on its territory.
In June, authorities in Bihac and Red Cross officials set up a new camp in Vucjak, the site of a former landfill ten kilometres from the city.
The EU refused to finance the centre which it criticised for being too close to minefields.
Some 800 migrants are currently staying there in ramshackle tents and with deplorable facilities.
"We are once again confronted with the increased arrival of migrants and refugees, which makes it increasingly difficult to ensure normal conditions for stay in this temporary camp," local Red Cross official, Selam Midzic, said Monday according to Fena news agency.