The 25-year-old midfielder, who joined from Sunderland in 2011 for ??16m, has emerged as an integral member of the Anfield side, featuring in all but one of their Premier League games last season.
The appointment was widely-expected after having deputised as captain in games for Gerrard last season, with Mamadou Sakho, James Milner or Martin Skrtel tipped to replace the England international as vice-captain.
Henderson told liverpoolfc.com: “I’m absolutely delighted and proud. It is a great honour and a huge privilege to be named as the captain of this football club.
“When Steven wasn’t in the team last season, I tried to do the best I could when I stepped in and took the armband. Now I’ll be looking to carry that on and continue to grow as a captain.
“I’ll look to give my best all of the time, put the team firmly first and try to give them – or help them with – whatever they need from me.
“I’ve learnt a lot off Stevie and how he conducted himself as the captain of this club both on and off the field.
“You’ll always learn from top players – and Steven was exactly that. I’ll use what I learnt from him to help me, but I also have to do things in the way I think is right.
“I’ll carry on from what I was doing last season and I’ll also try to take on more responsibility for the team and my teammates.
???We all have the same goal – and that’s to bring success to this club and our incredible supporters.”
Henderson has made 186 appearances for Liverpool in his four years so far on Merseyside, with 19 of those coming whilst wearing the skipper???s armband.
He had been the club???s vice-captain since last September and manager Brendan Rodgers believes he was a natural successor to Gerrard.
He added: “Jordan is someone who leads through example through his actions, attitude and application. He shows total commitment to the game and is a role model professional.
“He is also greatly respectful of the great traditions associated with being Liverpool captain and the responsibilities that come with it.
???He has been blessed to learn first-hand from one of the greatest the club has ever had in Steven Gerrard.
“Jordan has grown as a person and as a player since arriving at Liverpool and is ready to take up this challenge. He will be his own person, with his own style of leadership and his own ideas and methods.”