Despite being aged just 18, United were made to part with a reported £30m to secure the left-back's services.
However, despite that hefty fee, Albiston believes that United have made a smart acquisition.
"Obviously, he's a great addition to the squad. He's a top quality player. We've seen that in the last couple of seasons since he broke into the Southampton team at such a young age. Now he's taken it a step further by getting into the England squad and playing in the team," he told MUTV.
"He's only a baby in terms of league experience, but he's shown he can handle it by playing in the Premier League with no problem at all. He has fantastic physique about him. Some people find it a little bit difficult to settle in. He won't. He looks as if he's very level-headed and had a good upbringing at Southampton, a football club that seems to churn out a lot of good players.
"He seems to take everything in his stride. There is no weakness about him. You try to pick fault in people but he just does everything exactly right. Every pass seems to be perfectly weighted, he's a good tackler, you can beat him but he gets back because he's quick. I'm looking forward to watching him here."
It is believed that Shaw is the second most expensive signing in Man United's history