The much-protracted transfer sees Milner arrive at Eastlands in a reported £18 million deal, plus the £8 million-rated Ireland, with the England midfielder likely to make his debut against Liverpool next Monday.
Milner had been a target for Roberto Mancini for some time and the City manager's continued pursuit of the 24-year-old was thought to have played a role in former Villa boss Martin O'Neill's recent departure from the club.
After completing a medical late on Tuesday, Milner was at City's training ground and stadium on Wednesday to finalise the deal, which sees him take the No.7 shirt previously worn by the departing Ireland.
Mancini admitted he was delighted to finally capture a player who he has been tracking for months.
"I am very happy to have James with us, everybody knows we have admired him for some time," he said. "He is an excellent midfielder, who can play in a number of positions. This is important for the team, and I am looking forward to seeing him play for us. We have a very strong squad, and this signing is a very important one for us.
"James is already a very good player, who has proved he can play at the very top level. But he is also young and a good character, I think he can also improve and be a great player for Manchester City for a long time."
Asked if Milner was his final signing, Mancini said: "I think so. He is a good young player, who can play in every position in the middle and out wide.''
Milner said: "It didn't take too much selling by the boss (Roberto Mancini) when you see the players who are already here and the plans for the club. The last thing he said to me was 'be ready for the next game', and then he said 'be ready to win the Premier League', and that's my ultimate aim - that's what I want to do and why I'm here.
"There's a lot of competition to get there, it's where we all want to be. I'm ambitious and I want to win trophies here. I believe this is a great place to do that and I believe we will do it. Hopefully, sooner rather than later.
"The move seems to have gone on a long time - now all I want to do is get out on the field and play. I'm ready and raring to go now we've finally got everything done. I can't wait to start a new chapter.''
Ireland also completed his transfer to Villa, leaving after eight years at City. He emerged through the club's youth system, scoring 23 goals for the club and claiming the club's Player of the Year award in 2008-09.
Speaking on Ireland's departure, Mancini said: "I hope things go well for Stevie at Villa. He is also a very good player, and he has played a big part in City's history. I think he will enjoy the change of being at another club, and I hope he does well for Aston Villa."
Ireland is determined to rebuild his career at Villa.
"I have plenty of personal ambitions,'' Ireland told Villa's website. "I want to get back to playing the way I can - I haven't played 90 minutes in nearly eight or nine months, which isn't normal really for me. I've kind of forgotten the feeling what it is like to come off after a game feeling tired, winning or losing. I'm not used to sitting out for so long.
"So for me, I want to get back to playing at the top of my game and I want to work hard for my team-mates. I want to see if my team-mates and myself can push on and achieve something massive this season. Hopefully I can come here and build on that and help Aston Villa push on to better targets and reach higher goals. Hopefully I can be of benefit to the team.
"I think we have got a good bunch of young lads here who can go on and achieve something for themselves and for the club as well. We've got a very good squad. My number one target is to work hard for my team-mates, show them what I can bring to the table, show them they can rely on me and that I am going to work hard for them week in, week out.
"When I get my chance to get on the ball, hopefully I'll shine as well. I am really excited. I have only been here a day but I know what it is about already. It is a family club, I've seen a lot of happy faces here and a lot of friendly faces, so I am really excited for the future here.''
Villa caretaker-manager Kevin MacDonald was naturally disappointed to see Milner leave, but delighted to have Ireland on board. MacDonald said: "Stephen is a very talented young player who will complement the talented young players we already have.
"Hopefully Stephen will be as good for us as James was, and good luck to him at Manchester City. It's sad to see James go, but it's a great boost for the club that Stephen is coming in.''
Asked to highlight the differences between Ireland and Milner, MacDonald said: "Stephen's slightly different from James, but both are intelligent footballers. Stephen is a more inventive player who can link up with people, gets in the box and scores a lot more goals, and hopefully he'll do that for us.
"James has developed into a natural midfield player, Stephen has obviously played there most of his career, and from a young age. He probably understands the position a little more - not better - but a little more than James does, but they are two very fine footballers.''