The 26-year-old hot-shot has made 80 appearances for her national team, and joins until the end of the 2017 season, having featured most recently at Club level for French giants Paris Saint-Germain.
Skilful and quick with Champions League experience, the striker has drawn comparisons with superstar and compatriot Zlatan Ibrahimovic, and she's looking forward to showing what she can do in the FA WSL.
"It feels good to be here," she told mcfc.co.uk. "I'm impressed with the facility and the way the Club has built up this team.
"I really like that everything is in one place - the men's team, the women's team and the youth teams. It's amazing that the women's side are able to create this environment.
"The main thing that made me want to come here is the way the Club declared their ambitions.
"PSG are a huge club and I learned a lot there - they're trying to do similar in taking the women's side to the next level - but here, it feels like the future.
"This team has a lot of potential and ambition. They want to win titles and I want to help them to do so."
Though born of Kosovar-Albanian descent, 'Kosse' represents the Swedish national team, having been born in Kristianstad, after her parents migrated.
She grew up with two passions - football and ice hockey - but opted to pursue a career in the former. At 15 years old, she joined Vimmerby IF and netted an astounding 49 goals in 48 games, attracting interest from several top-flight sides.
In 2007, she signed for Damallsvenskan outfit Linköpings FC, becoming a first-team regular the following season.
She went on to help the Club to its first league title, plus the Svenska Cupen, before realising her dream of visiting the USA when Chicago Red Stars snapped her up in December.
After a year in the States, Asllani returned to Linköpings, who were competing in the Champions League. The striker found the net in the competition with goals against Sparta Prague and Arsenal, but a thigh injury hampered her campaign and she moved to her hometown side for a season.
It wasn't long until Europe's elite would come calling for Kosse, and the forward signed for PSG in 2012. Her debut campaign heralded 17 goals in 19 appearances, and she would go on to net 45 times in all competitions for the French outfit.
Driven, dedicated and eager to improve, the striker has often expressed her desire to be the best in the world, and hopes her past experiences can benefit the Blues.
"Coming here and being able to play for a team like City is amazing," she added. "I'm going to do everything I can to help the team win titles.
"I'm a technical player that likes to have the ball and create chances for my team.
"The English league is growing a lot. I'm curious and that's why I'm here.
"I feel I can help the team to be the best. I wouldn't want to go to a team that doesn't strive for the best."
With plenty of experience in Europe's top competition, including an appearance in last year's final, Asllani believes the Blues have what it takes to compete at the highest level.
"The Champions League is something every team strives to win," she stated. "It's going to be tough but it will be interesting to see how the team do.
"They came second [in the league] last year and were close to winning it, so I think this team can surprise in the Champions League."
Reflecting on his latest capture, manager Nick Cushing declared: "We’re delighted to sign a player of Kosovare's calibre. She’ll add another dimension to our squad.
"We admire her passion and ambition - it matches everything this club stands for - and we're really looking forward to working with her."
You can see Kosovare and the rest of Manchester City Women’s squad in their pre-season friendlies against Rosengard and Pitea IF. Click here for more information.
Seasoncards for 2016 are also now on sale.
Be part of the action as the team challenge for silverware on four fronts, including the UEFA Women’s Champions League for the first time in the Club’s history. Click here for more details.