The project is part of Strathclyde Partnership for Transport's (SPT) multi-million pound overhaul of all of its 15 stations in the city across the next six years.
Graham was appointed to the framework for the scheme along with Sir Robert McAlpine and Clancy Docwra with each contractor then bidding for parts of work.
The Ibrox overhaul is due to start in March and will see all walls, floors and ceilings replaced.
Information and signage for passengers is also being improved while more efficient lighting is being installed.
Better facilities for disabled passengers, a new station office and work on the exterior of the building will complete the makeover.
Graham said up to 30 workers will be on site during the busiest phases with all work scheduled to be finished prior to the Commonwealth Games starting in 2014.
The subway will continue to run with the majority of work being done when it is closed and passenger access should not be affected during the revamp.
Graham Construction regional director Gary Holmes said: "Graham has a real track record of working on transport projects, including the trams network in Edinburgh and the redevelopment of St Pancras Station in London.
"We are therefore extremely proud to be part of the team delivering the upgrade of the stations on the Glasgow Subway system and look forward to starting work on our first project at Ibrox."
Graham Construction is a privately owned company with Northern Ireland headquarters.
It has operated in Scotland for more than 20 years and has offices in Glasgow, Edinburgh and Aberdeen.
For 2012 its turnover in Scotland was reported to have been around £150m while it employs around 400 staff here.
SPT's subway modernisation programme started at Hillhead and has also included Partick and Kelvinhall.
The near £300m programme – which includes new escalators and lifts plus smart card ticket technology – is expected to be completed before 2020.
SPT has estimated the upgrading could lead to reduced operating and maintenance costs over the next 30 years.