The 31-year-old England forward, who has joined the Black and Whites on a three-year contract from NRL side Wests Tigers, takes over the role from Andy Lynch.
"It has been a difficult decision," said Hull coach Peter Gentle, who has appointed Hull-born hooker Danny Houghton, 24, as vice-captain. "Andy has done a great job for us in a testing year at times but we felt that we were going into a new era for the team and a fresh start for everyone and Gareth seemed like the perfect candidate."
He added: "We've been watching all the players closely over pre-season and his leadership qualities and experience stood out, having played in Super League, the NRL and internationally.
"He is a strong character, a natural leader and instils a culture around the club that we feel is very important and, having seen how he has fitted into the squad, we felt he was a natural captain."
Ellis, who will lead his new team for the first time in next Friday's Super League opener against his former club Leeds, described his appointment as one of the proudest and most humbling moments of his career.
"It is a fantastic honour and one I won't take lightly," he said. "I've seen already what this club means to the players, the staff and the fans and to be named captain is a special achievement.
"You only have to look at some of the names who have done it before to realise what sort of company you're in, people like Johnny Whiteley, Clive Sullivan, Steve Norton, David Topliss - they're all legends of the club and the game.
"Even more recently I recall the likes of Jason Smith and Craig Fitzgibbon as captain and these are some of the game's best players, so to be on the list is very humbling.
"It will be a very special moment to lead out this team at Headingley but that is something I can reflect on in years gone by. The only thing we're thinking about right now is the match, producing our best performance and claiming our first two points of the competition."