Ruddock was one of the favourites to take over from Hansen who will leave the post at the end of the RBS 6 Nations championship in the spring.
Despite the off-field problems which have dogged the Dragons, the team have exceeded expectations on the field.
Ruddock said: "I am really enjoying being part of the Dragons and the way the squad has pulled together during our off-field problems has had a big bearing on my decision not to apply for the Welsh coaching position.
"The Dragons team and coaching staff have put their heads down and got on with the job in hand doing their talking on the field. The adversity we faced off-field has created a special bond between the Dragons squad and the management team. This bond would be particularly difficult to break at this time."