Wilson, who started his career at Ibrox in 2008, was the Hearts skipper last term as he led them to the Scottish Championship title
He ended his stay at Tynecastle when his contract expired last month and has signed a three-year contract with Rangers.
Weir believes the 23-year-old has the attributes to follow in his own footsteps and wear the armband.
The 45-year-old, who played alongside Wilson when the centre-back first broke into the Ibrox team as a teenager, told RangersTV: “I think you forget how young he was when he was playing here the first time and obviously he’s gone
down south and had various clubs there.
“He played for Liverpool and he was out on loan at Bristol (City) and a couple of other places. So he’s learned a lot and he’s matured a lot.
“Meeting him in the last few days again you can see he’s grown up and he’s developed physically and mentally so he’s a different lad to what he was, although he’s still got a lot of the same characteristics. He’s a nice person, which helps as well.
“As I said he does tick a lot of the boxes and that being another one as well, the fact he is vocal, he is a leader and he’s a potential captain.
“He’s one of those types that are few and far between so that’s another added bonus with getting Danny here.
“He’s got the attributes to come in and be the right type of person, set the tone for everyone else and be a part of what we want to do here.”