The ribbon was cut by the Prime Minister of the Federation of Bosnia and Herzegovina entity, Nermin Nikšić, and Federation Transport and Communications Minister Andrijana Katić, after which there was a fireworks display.
The bridge, which spans the River Neretva at Počitelj and was named Herzegovina, is part of a new, 11-kilometre highway section that is an integral part of the Vc corridor and connects to Croatia's A1 motorway, with an exit to the port of Ploče.
BiH Prime Minister Borjana Krišto said the inauguration of the bridge was a historic event for BiH.
"The bridge... is a crucial point of transport connectivity between BiH and the EU," said Krišto, thanking PM Plenković, who is on a two-day visit to Bosnia and Herzegovina, for his support to the neighbouring country.
BiH Federation PM Nikšić said that the new Federation government had made an important step towards dynamising the construction of transport infrastructure, thanking PM Plenković for his support for the opening of accession talks between the EU and BiH.
"Without your engagement and that of other friends, that would not have been realistic," Nikšić said.
The Herzegovina bridge is 980 metres long and close to 100 metres high. The cost of its construction is slightly more than €100 million.
Earlier in the day, Plenković held meetings with a number of senior BiH officials and attended a session of the BiH Presidency.
On Thursday, he is scheduled to meet with Croatian National Assembly of Bosnia and Herzegovina (HNS BiH) leader Dragan Čović and visit several important institutions.