The former England Sevens wing also scored twice against Warriors during the regular season, including a stunning solo effort from inside his own half in the fixture at Sixways.
Born in Suva in Fiji, Drauniniu joined the Royal Navy in 2003 at the age of 17 and saw active service in the Gulf in 2005. Drauniniu was soon introduced to rugby union, having played rugby league and football at school in Fiji, and he made his debut in the annual Army versus Navy match at Twickenham in 2004.
Three years later the 25-year-old was signed by Exeter Chiefs, where his pace on the wing caught the eye of the England Sevens selectors. He scored a sensational try on his international debut against Portugal in Dubai in 2008.
Drauniniu was named in Rugby Times' National League One Team of the Season for 2008/09, having scored 16 tries. In his first season he had raced in for 22 tries, and it was that sort of form that alerted Harlequins to take him to the Premiership.
His first start for Quins came in a 9-9 draw with London Irish at the Stoop in October 2009, but the highlight of his spell at the club would come at Franklins Gardens three weeks later when he scored two tries as a second half replacement in a 27-16 defeat.
In February 2010 he forced his way back into Ben Ryan's England Sevens team for the Adelaide and Hong Kong legs of the IRB World Series.
Head Coach Richard Hill said: "I first saw Josh playing for the Royal Navy three or four years ago, while he was at Exeter, and he was the standout performer. He was a raw talent and a real try scoring machine that I have tracked ever since.
"This year he has had a particularly strong season for London Welsh and has been up with the best of them in terms of scoring tries and has matched the likes of Miles Benjamin and Marcel Garvey. We want players like Miles and Marcel who are try scorers and who can out of nothing explode into life.
"When he has played against us this season he has been a real thorn in our side and so we are delighted that he will now pull on a Worcester jersey next season.
"Both Josh and Errie Claassens have really benefitted from the style and positive attitude that London Welsh have adopted throughout this season and hopefully the move to Warriors will see them get even better."