The 23-year-old signed a four-year deal at Villa Park for an undisclosed fee after attracting interest in his 52 games for the Blades.
Lowton told the club's official website: "It's every boy's childhood dream to play in the Premier League and it was one of mine.
"This opportunity is fantastic and I thank the manager for giving it to me. Hopefully I can repay the faith that's he's shown in me and keep going at a higher level.
"Just from driving up to the training ground you can see the difference in the quality of things. The training ground looks spectacular and the pitches look phenomenal.
"It's a massive club in the Premier League with a big fan base and I'm looking forward to getting to work as soon as I can.
"I played the majority of last season at right back but I have played right midfield and central midfield as well.
"I think my main asset is going forward and my technical ability but obviously I'm going to try and add whatever the manager is after from me.
"These are exciting times for me and I can't wait to go out and start playing."
Lowton admitted he was flattered with the interest from Paul Lambert, and he hopes the quality already at the club can help this coming campaign to be a top one for Villa.
The 23-year-old said: "It's fantastic to think I'll be playing under Paul Lambert. I was flattered when I heard the interest and, when speaking to him, he's helped me settle in nicely so far.
"Hopefully we can get on well and I can fight for my place and play a few games this season.
|33/1||Aston Villa are 33/1 with bet365 to win the League Cup next season.|
"As a League One player last season, Premier League players are what everyone looks up to. Seeing guys like Darren Bent and Gabby Agbonlahor and people like that is fantastic.
"Meeting players who have played international and Premier League football all their lives is amazing.
"You can sense the buzz around the place at the moment. The lads were all having a laugh and joke when I came in this morning and they've all been very welcoming which was very good of them. It's a new era with the new manager and a few new signings.
"The squad has already got some fantastic players, everybody knows them so hopefully we can all come together and have a successful season."
Aston Villa boss Paul Lambert was also delighted to welcome Lowton to Villa Park, and the former Norwich City manager believes he has sufficient motivation to help push the Brimingham-based club forward this season.
"Matthew is a really talented young player who brings a lot of things that can really benefit the club," Lambert said.
“He's a good player already and he's only young so he has the potential to be a really good player for us.
"He's hungry to succeed and to go further in the game, both of which are attributes that we want at this football club and that we are looking for.
"We won't put any pressure on him, we just want him to go out and enjoy playing.
"What he's done so far at Sheffield United has been great so hopefully we can progress him a bit and he'll do very well for us."