Goffin, the world number 15 who has won the two Davis Cup matches he has played this year, will start as favourite on the hard court in Brussels against the 65th-ranked clay specialist Delbonis.
Argentina's top player Leonardo Mayer will face Steve Darcis in Friday's second rubber. Darcis won their only ever previous meeting four years ago.
Belgium last reached the Davis Cup final in 1904 and they lost it 3-2 to France at Wimbledon.
Argentina will be playing their 10th semi-final in 14 years, although they have won only four of those ties and then lost each time in the final.
(Reporting By Philip Blenkinsop; editing by Clare Lovell)
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