The work will start in August 2022.
Accessible lifts will also be added to the Grade II listed footbridge.
Passengers who need assistance can currently only access platforms 2 and 3 via a crossing over the tracks when station staff are available. The upgraded footbridge will give travellers more independence and improve the overall experience.
Matt Rice, Route Director for Network Rail's North and East Route, said: "When the new lifts are in place, rail passengers in Selby will have the freedom to access all platforms at all times and enjoy hassle-free journeys.
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"While step-free access is a must-have for the future of the railway, we also know how important it is to preserve our heritage. Strengthening the footbridge will make sure the station’s iconic style is kept intact for years to come."
The final designs for the Access for All scheme began in January after receiving listed building consent from Selby District Council.
Nigel Adams, Member of Parliament for Selby and Ainsty, said: "Improving access to Great Britain’s railway stations is a key priority for this Government; we want all passengers to be able to travel easily and confidently.
"Having supported the application for funding to upgrade Selby station from the outset, I am delighted that work will start soon. The upgrade will be done sensitively and will incorporate the iconic footbridge. Selby station is one of the 73 stations that received funding in 2019 as part of the Access for All Programme."
