His first recording came with the 1987 Chandos release of the Khachaturian piano concerto, with Neeme Järvi leading the Scottish National Orchestra. By 1990, Orbelian had appeared with a varied and impressive list of orchestras, including the Boston Symphony Orchestra, the Detroit Symphony Orchestra, the Moscow State Symphony Orchestra and the Moscow Chamber Orchestra. He had also done some conducting by then, but only infrequently, and on the occasions when he did he usually led the ensemble from the keyboard.
Favorably impressed by his pianistic and conducting skills, the Moscow Chamber Orchestra management appointed Orbelian music director of the Moscow Chamber Orchestra in 1991, following the death of conductor Andre Korsakov. Orbelian was the the first American ever to hold such a position in Russia. In 1992, Orbelian and his wife, violinist Maria Safariants, founded the Palaces of St. Petersburg Festival. Safariants, who lives in St. Petersburg with the couple's son, is the director of the event, which is held every June. In 1998, Orbelian took the M.C.O. on a highly successful concert tour of the United States, covering 50 cities. They appeared three times at Carnegie Hall between 1998-1999. Most of Orbelian's recordings have been for the Delos label, but he has also recorded for Chandos and Philips. Some of his other efforts include the 1999 release of works by Piazzolla, on which he led the M.C.O., and a disc of Tchaikovsky works entitled Queen of Spades -- Great Scenes, on which he conducts the Russian Philharmonic Orchestra. Both CDs appear on the Delos label. In 2000, Orbelian was named permanent guest conductor of the Moscow Philharmonic, and in 2004, became the first non-Russian citizen to be given the title "Honored Artist of Russia," with the award bestowed by President Putin.