Henderson inherited the Reds captaincy when Gerrard departed Anfield in 2015.
The 29-year-old made his 100th appearance as Reds skipper in Saturday's win over Arsenal, and Redknapp was full of praise for the England international.
"Jordan Henderson taking over the captaincy from Steven Gerrard was up there with the toughest of jobs in football. It was like taking over from Sir Alex Ferguson as Manchester United manager," Redknapp wrote for the Daily Mail.
"You don't want to follow the man. You want to follow the man who followed the man.
"I know what the pressure of pulling on that armband is like. A lot of people might just see the letter 'C' alongside a name on the team sheet and think nothing more of it. You do when you are the captain of Liverpool football club, believe me.
"He won't have taken being named the new leader of this club lightly, especially after taking over from a legend like Gerrard.
"Henderson was under pressure. There was expectation on the England midfielder, and he got a lot of stick at times. He had his haters, but he has hushed them all.
"I have never been to watch my former side and left thinking Henderson did not have a right good go. At the very least, he puts in a shift. You can always count on him to give his all."