Hill, 18, scored 15/16 in the skeet final to beat Thailand's Sutiya Jiewchaloemmit.
Scott, 30, triumphed in the double trap, shooting 27/30 to beat Qiang Pan of China.
"To come away with a gold is an amazing end to the year and I couldn't have asked for a lot more," said Hill, who won gold at the European Games in June.
Amber Hill and Steve Scott both won gold medals at the 2015 ISSF Shotgun World Cup final in Cyprus.