Rodgers convinced Henderson to sign for the Reds from Sunderland while in charge at Anfield.
“There was a lot of interest in Jordan so I invited him around and chatted," Rodgers told the Telegraph.
“I said to him, 'Jordan, you are going to be the next captain of Liverpool'.
“That was it from there. We spoke about moving forward. It was a natural move for him as Steven Gerrard was preparing to leave. I knew he would be a captain the club would be proud of.
“It was an emotional meeting. He knew it was an honour to captain a club the size of Liverpool, and knew where he had come from. He has had to work for absolutely everything.
“I always liked Jordan as a guy. He is honest, dedicated and always wants to make himself better. I had already made him vice-captain so he could get a sense of the responsibility of leading, and then when Stevie left Jordan had become such a prominent player he was in position to take over."
Rodgers also thinks Henderson has grown into the role of Liverpool's leader.
“He is really selfless as a player and a guy, always wanting to help those around him. He builds respect around himself," he added.
"He always wanted to improve. He would do extra on the training field, working on set-pieces, practising the whip he could get on the ball where – as you can see now - he delivers it really well.
“Off the field he is super professional. I never saw him have a drink, or if I did he was never drinking much.
“It was always going to be difficult for the guy who took the Liverpool armband from Stevie. It was always going to take time. Jordan is his own character. He has really developed superbly as a captain and player."