As troops stood guard, Austrian President Heinz Fischer and his wife Margit greeted the royals in the inner courtyard of Vienna's Hofburg Palace.
After an inspection of the military, the two couples headed inside, where they were welcomed by a group of singing school children wearing bright yellow shirts and waving Austrian and Swedish flags.
The royals have a tight schedule through Thursday. Tuesday's program includes a tour of Vienna's famous Albertina museum, a stop at a Swedish church and a visit to Austria's parliament. A state banquet is slated for the evening.
On Wednesday morning, Carl Gustav will take part in an Austrian-Swedish economic forum, as well as a seminar on renewable energy sources. Silvia, meanwhile, will start her day at the Jewish Museum, followed by a visit to a Swedish design exhibit. She is also expected to give a speech about children's rights.
Following a lunch hosted by Austrian Chancellor Alfred Gusenbauer, the royals will head to Vienna's United Nations complex Wednesday afternoon, where they are expected to meet a range of high-level diplomats, including Antonio Maria Costa, executive director of the U.N.'s Office on Drugs and Crime and Mohamed ElBaradei, head of the International Atomic Energy Agency.
Before heading home, the royals will visit the Austrian province of Burgenland on Thursday.