Concerns were raised for the 43-year-old ex-wing on Sunday after he failed to return home after being out with friends on Saturday.
His Toyota Hilux was recovered downstream from Abberwick Ford on the River Aln outside Alnwick, Northumberland, and police suspected he was swept away while trying to escape the vehicle.
The river level was particularly high at the weekend when Storm Darragh lashed the UK.
A major search operation was launched involving Northumbria Police, drones, the police helicopter, coastguard officers and the North of Tyne and Northumberland National Park Mountain Rescue Teams.
Family and friends of the much-loved former rugby player also joined the search.
Northumbria Police said they faced "very challenging conditions, not least due to the river flow and the level being significantly heightened after the exceptionally heavy rain experienced over the weekend".
On Thursday, specialist officers from Northumbria Police's Marine Unit made the sad find in the river near Abberwick Mill.
The force said formal identification was yet to take place but Voyce's next of kin have been notified and were being supported by specialist officers.
Chief Superintendent Helena Barron, of Northumbria Police, said: "This is an extremely sad development and our thoughts very much continue to be with Tom's loved ones.
"I would like to thank all of our officers, partners and volunteers for their assistance throughout the searches which have been conducted in very challenging circumstances.
"We would continue to ask that people respect the family's privacy at this time."
Officers do not believe there to be any third-party involvement and a report will be prepared for the coroner.
The world of rugby expressed its shock and sadness when he went missing, including messages from World Cup winners Matt Dawson and Lawrence Dallaglio.
Voyce won nine caps for England during his career and spent six years at Wasps, from 2003 to 2009, helping them win European and domestic titles after moving there from Bath and then leaving to join Gloucester in 2009.
He made 220 Premiership appearances before retiring in May 2013.
It was understood Voyce, who was raised in Cornwall, relocated to Northumberland recently after living in London.
