The newly expanded Reading station has capacity for the service and a route has been identified for faster trains when Crossrail fully opens in 2019.
The previous terminus for Crossrail was Maidenhead.
The government said only “minor works” would be needed to accommodate the extended service.
Rail minister Stephen Hammond said: “Crossrail reaching Reading is further proof of our commitment to deliver a transport network fit for the 21st century.
“It will improve connectivity and deliver greater choice and convenience for passengers travelling into London.
“It will also make better use of the already congested Great Western Main Line, freeing up capacity for further improvements including potential direct services from Reading to Heathrow as part of the western access scheme.
“In addition I have requested Network Rail to look at the cost benefit analysis of increasing the number of faster trains between Reading and Paddington.”