Urbis, which cost £30m, is housed in a striking new building made entirely of glass, which rises more than 110 feet above Manchester city centre.
The museum, next to Victoria Station, contains dozens of interactive displays that take visitors on a tour of cities around the world.
The museum's director, Elizabeth Usher, said the main aim was to ensure visitors had fun.
The centre houses extensive databases and archives of videotape, which are used on interactive displays spread over four floors.
Ms Usher said: "We're part of a group of organisations that are trying to ensure that visitors have a lot of fun and can engage with ideas over many different levels.
"The actual building is so dramatic, it's totally awe inspiring.
"We're using hands-on interactive technology to enable people to really understand the experience of living in cities in different parts of the world."
CCTV focus
The displays include sequences of historic images controlled by visitors walking along a "time line".
Children can also see if their faces have been spotted by hidden cameras as they walk around a section focusing on the use of CCTV in cities.
The exhibits let visitors explore life in a range of cities across the world focusing especially on Manchester, Los Angeles, Sao Paolo, Singapore, Paris and Tokyo.
Architect Ian Simpson said: "What we've done is to create a building that is both opaque and transparent.
Lottery cash
"We wanted to create lots of views and interesting changes within the skin of the building, both from the inside and around the city.
"The building changes with the climate - when it's sunny it's reflective and at night time the whole building becomes transparent and glows, giving something back to the city."
The project has been funded largely by Lottery cash with some public money.
Manchester City Council has pledged £1m of local council taxpayers' money to maintain the museum.