The two entrances will comprise of glass canopies.
The structures are part of a wider £5.3m scheme to redevelop the city station and have been commissioned by Strathclyde Partnership for Transport.
When completed, the entrances at Argyle Street and Howard Street will feature glass structures that have been inspired by Kibble Palace in Glasgow's Botanic Gardens.
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Graham Construction is undertaking the work and has said it expects to complete the project by summer 2015.
Gordon Maclennan, Chief Executive of Strathclyde Partnership for Transport, is quoted as saying: "Modernisation of the subway is progressing at pace and the redevelopment of St Enoch Station is one of the most exciting aspects of the project so far.
"Passengers have benefited from the internal improvements made to date and we're confident that everyone using the station will enjoy the striking new look station exterior.
"I'm looking forward to seeing the station completed as it is a stunning design and will, I'm sure, become a striking centrepiece to the wider area."
(JP/MH)
