Like Wales, Romania missed out on World Cup qualification after losing their play-off semi-final in March.
The match in Bucharest will be the first meeting between the teams since 1993, when Wales lost at home to Romania to agonisingly miss out on the 1994 World Cup.
This will also be a first home match in charge for the great Gheorghe Hagi, the former Barcelona and Real Madrid playmaker who scored in Cardiff 33 years ago.
Hagi was appointed Romania’s manager for the second time in April, taking over from Mircea Lucescu, who died at the age of 80 following a heart attack.
Ghana, meanwhile, will be facing Wales for the first time and have Manchester City’s Antoine Semenyo in their squad.
Former Manchester United assistant manager Carlos Queiroz was appointed Ghana’s head coach last month.
The 73-year-old Portuguese has replaced Otto Addo, who was sacked in March after friendly defeats by Germany and Austria.
The Black Stars, who are in the same World Cup group as England, Croatia and Panama, also failed to qualify for the 2025 Africa Cup of Nations under Addo.
The matches against Ghana and Romania will serve as preparation for Wales’ return to the top flight of the Nations League in September, where they have been drawn with Portugal, Norway and Denmark.