South West Trains said extensive repairs to the line should be complete by the close of today, allowing the full re-opening of the route on Monday.
It followed the removal yesterday of wreckage from Friday's accident, in which a handful of people were injured.
The incident happened when the lorry, travelling towards Leatherhead, Surrey, crashed into the wall of a bridge in Warren Lane, Oxshott, at about 3.30pm.
Part of the wall subsided, causing the lorry to plunge on to railway tracks bellow.
At the same moment, an eight-carriage train bound for London Waterloo was passing underneath.
The lorry bounced off the roof of one of the carriages, causing it to partly cave in, and came to rest on the embankment.
Emergency teams said it was remarkable that nobody was killed in the incident, but several people were injured.
The driver of the lorry and one of the train passengers were said to be in a stable condition at St George's Hospital in Tooting, south London, yesterday.
Both were badly hurt in the incident.
Other people with less serious injuries were treated at the scene.
The focus of the investigation into the crash is expected to focus on why the wall failed to stop the lorry from landing on the track.
Resident Stuart Mellstrom, who has lived next to the bridge for 40 years, said he had written to Elmbridge Council several times regarding his concerns over traffic volume in the area.
He said: "It's a miracle that, as far as I know, there has not been a fatality to date. This is an accident that has been waiting to happen, although it hasn't taken the format that I anticipated. But I have seen so many accidents in this area it is beyond belief."
He said lorries using the bridge were too heavy and too large.
"This is a Victorian bridge built for light railway and light traffic," he said.
Despite the track being repaired, users of Oxshott rail station have been warned to allow extra time for their journey due to traffic build-up resulting from the damaged bridge.
Andy Pitt, managing director of South West Trains, said: "We are pleased our customers on the line serving Cobham, Oxshott, Claygate and Hinchley Wood will have their full normal train service restored tomorrow morning.
"We would like to thank British Transport Police, the site teams and engineers from Network Rail for their support and hard work in clearing the track and making the line safe to re-open.
"We will have staff on site at the stations affected by the recent disruption to give advice and assistance and we would once again like to thank our customers for their patience and understanding.
"Our thoughts continue to be with those injured."