Additions will include a new ticket office, ticketing machines and ticket gates (including wide aisle gates), lifts to the platforms and another stairway.
More than 60,000 passengers currently use the Hammersmith & City station every day, with demand growing as a result of the extension of the Circle line to Hammersmith.
When Crossrail services begin in 2018, passenger numbers will increase further.
Paddington station will be a key point on the Crossrail route as it runs through central London. Twenty-four trains an hour in each direction will pass through the station during peak periods.