It had been due to open on 6 October, but was delayed while Network Rail worked through a "snagging list".
Area director Terry Strickland said the delay had been "frustrating," but that the station would be a "fantastic addition" to the town.
Northampton South MP Brian Binley said "bad publicity" had pushed Network Rail into solving the problem.
Operator London Midland said it had started working to move staff and equipment into the building. The company said the process normally took three to four weeks.
London Midland's head of West Coast Services, Terry Oliver, said "Our priority now is to get the station ready for our passengers."
Mr Binley, who had called Network Rail "ill-mannered and arrogant" and threatened to raise the delays in Parliament, said: "One of the people I met with gave the game away when she said, 'I am really unhappy about the bad publicity you have created for us'.
"Sometimes you have to play your cards in a pretty robust fashion."
The 2,500 sq m station building is twice the size of the old one. Firms including Starbucks, Cafe Republic, WH Smith and Enterprise car rental will move in, while new lifts and an over-bridge to cross platforms will open on Monday.
The much-delayed Â£20m Northampton railway station will open no later than 12 January, Network Rail has announced.