Henderson, 24, enjoyed his best season yet in 2013-14 and replaces the departed Daniel Agger as Steven Gerrard's deputy.
Rodgers, whose side face Ludogorets in the UEFA Champions League on Tuesday, said the England international had a bright future ahead of him.
"Jordan is someone who represents the best values of what we are all about, as a team and as a club," Rodgers said.
"Both he and Steven are examples to others in how they conduct themselves on and off the pitch.
"It's how they live their lives, it's how they train and it's how they approach their work.
"Jordan is completely dedicated to the game and his leadership qualities come from the example he sets. It's another great story for Jordan in his journey as a Liverpool player and it shows the great progress he has made.
"For club and country he holds himself really well, he's got great stature and I believe he will be an important player here for years to come."
