Woods will replace Simon Crookall, who left the RSNO at the beginning of the year to become president and CEO of the Indianapolis Symphony.
"When I came to the NJSO, my intention was to stay for a significant period of time," Woods, a Briton, said in a statement. "But when the offer arose from the RSNO I realized that, after eight years in this country, a move back to the U.K. was the right decision for me and for my family."
Much of Woods' tenure at the NJSO was dominated by the controversy over the orchestra's purchase, before his arrival, of a group of rare string instruments from philanthropist Herbert Axelrod. The instruments were later judged to be overvalued, and an internal report criticized the orchestra's handling of the purchase.
Before coming to New Jersey, Woods was vice president of artistic planning and operations at the Philadelphia Orchestra for seven years. He was previously a record producer for EMI Classics in London.