The 29-year-old full-back, who missed the second half of last season with a foot injury, takes over the reins from the departed Jason Forster.
"I believe Kevin is a natural successor as captain and there is no doubt in my mind that he will do a great job," said Dragons head coach Paul Turner.
"He has a hard act to follow on the back of last season's captain Jason Forster who I would again like to thank for his efforts as captain.
"Kevin is a motivator of men, an excellent communicator and on field inspires those around him.
"He has the respect of all the players, leads by example and has the best interests of the team at heart, there is no doubt he will prove to be an inspirational and tremendous captain."
And he will probably have to use those motivating skills as the Dragons are having to play in the European Challenge Cup after failing to qualify for the Heineken Cup at the end of last season.
"We are in a rebuilding process," conceded Turner, "and we see Kevin as instrumental to taking us forward."
Morgan, who has 36 Wales caps to his name, joined The Dragons for the 2004-2005 season from the Celtic Warriors. He has played 34 times for the Dragons and has scored 15 tries.
"I am very proud to be made captain of The Dragons," commented Morgan.
"Last season is now behind us and the whole team is looking forward to the challenges ahead. There are a number of new faces who will make an impact.
"The support we had last season was tremendous and with the backing of our supporters I can assure fans that on-field we will be doing everything we can to repay their support."