Work on footpaths, the carraigeway and the car park was due to start on Monday this week (February 1).
Now it won’t begin until later this month and will last approximately seven weeks.
East Dunbartonshire Council is creating a Sustainable Travel Hub - which aims to make it easier to connect journeys whether you are travelling by train, bike, bus or car.
Some parking provision will be limited while works take place, but this will be kept to a minimum.
Work is taking place as part of the A81 Route Corridor Improvements and is being paid for through Transport Scotland’s Bus Investment Fund.
As well as working on the car park, old slabs will be replaced with high-quality granite. The aim is to create a welcoming gateway to the town centre and encourage footfall.
There are currently 133 spaces - including seven disabled bays. That will be temporarily reduced to around 75 during works. When work is completed there will 135 spaces, more bike racks and greater access for all.
Councillor Alan Moir, convener of development and regeneration, said: “There has been an unavoidable delay in starting works due to recent heavy rain and high winds impacting on our contractor’s schedule.
“However, I am pleased that we will soon be investing in our car park at Milngavie Station, as well as carrying out footpath improvements.
“This investment will prioritise pedestrian movement, while enhancing parking facilities and encouraging greater use of public transport.
“The project is part of a wider scheme to encourage greater active travel movement and economic opportunities in Milngavie.
“Promoting sustainable transport is a priority for this council - helping people to lead healthier lives, cutting down on carbon emissions and improving the environment.”
Scotrail, Abellio and Network Rail have been key stakeholders during the Milngavie Station design process, alongside Strathclyde Partnership for Transport and First.
Kessington Travel Hub was created in Bearsden last year, with associated footpath, carriageway and signal improvements to make it easier for people to shift in travel modes.