The summer addition will provide back-up to Jordan Henderson, who was given the armband last month following the departure of Steven Gerrard to LA Galaxy.
Milner has impressed during pre-season, earning the admiration of both his team-mates and the Reds boss.
Rodgers told reporters: “He is someone I admired from the outside for a long time. He’s played at this level since he was 16 years of age and has played for some fantastic clubs.
“He went to Man City and did a great job and when the possibility he was going to be available, obviously you’re surprised but then you’re hoping you can get him to come to your club because he’s the type of player who gives everything.
“His actual football talent has probably gone under the radar because he’s played around some outstanding talents, but this is a guy who works tirelessly at his game.
"He’s in here at 7.45am in the morning making sure he’s prepared for his training, getting all of his food supplements and getting everything correct before training – he’s in two-and-a-half hours before he trains and then does his work, gives his maximum. He prepares himself like an elite player should.
“He’s also got big character and a big mentality, and I felt we needed that in the team to the extent where he will be the vice-captain this year.
“Jordan has been appointed the captain, but he’ll be a great ally for him because he leads by example. James is a wonderful, wonderful footballer and a big personality in the dressing room as well.
“His commitment, his qualities, how dynamic he is on the training field and how demanding he is of other players. That in terms of the captaincy and vice-captaincy can work really well for us.”
Liverpool lost 6-1 against Stoke on the final day of the 2014-15 campaign, a result Rodgers is keen to avenge on Sunday.
“We will certainly be better than where we were last year,” Rodgers added.
“That was a one off game. It was incredible how we were lacking in every aspect of football. A score like that should never happen, sometimes it does, but it was more the way it happened.
“I stood there and it wasn’t comfortable. The reaction over the course of the summer has been terrific. It gives us real motivation. I feel we couldn’t have had a better fixture. It is the perfect fixture to go away to Stoke.”
