Cambridge North has a 450 sq m (4,843 sq ft) building, three platforms and parking for 1,000 bikes and 450 cars.
Trains travelling between Ely, London and Norwich will stop at the city's second station.
Its silvery cladding is based on the computer model Game of Life, created by mathematician John Conway while he was a lecturer at Cambridge University.
For years, the Princeton professor felt the game overshadowed his more important achievements but now said he has grown to like it.
The mathematical model was published in Scientific America in 1970 and helped launch a new branch of mathematics.
Cambridge North, which is close to the city's business and science parks, has been built without a manned ticket office.
In 2019, a direct service to Stansted Airport will be introduced.
It was due to open in December 2015, but this was put back to May and then to December 2016.
The city's first railway station, which is in the southern part of Cambridge, opened in 1845.
A £50m railway station whose opening date was put back twice is finally running services.