Virgin Trains and French rail operator SNCF will jointly bid to run services on the new high-speed route between Birmingham and London.
The companies have announced they are entering the competition for the newly formed West Coast Partnership franchise.
The Department for Transport announced in November that initial services on the new HS2 line would be operated by the same company running the InterCity West Coast franchise.
The current franchise, which runs from London to Scotland via the West Midlands on the West Coast Main Line, has been operated by Virgin Trains since its formation in 1997 and expires in March 2018.
But the new West Coast Partnership will operate both the InterCity West Coast franchise from April 2019 and HS2 services for the first three to five years of operation, from 2026.
If the Virgin Trains/SNCF bid is successful, it would increase the proportion of Britain's rail franchises run by overseas operators.
Half of the partnership would be owned by Stagecoach, with SNCF taking a shareholding of 30 per cent and Virgin 20 per cent.
Virgin Trains is currently owned by Virgin (51 per cent) and Stagecoach (49 per cent).
Stagecoach Group chief executive Martin Griffiths described the partnership as "world-class" as it combined "the team which has transformed intercity rail travel in the UK with the most recognised and capable high-speed operator in Europe".
SNCF has operated France's intercity TGV service since 1981 and runs around 700 high-speed journeys each day - in France and internationally - at speeds of up to 200mph.
The company's existing involvement in Britain's railways is through its 70 per cent ownership of transport group Keolis which itself has a 35 per cent stake in Govia.
Govia owns London Midland which operates one of Birmingham's main commuter routes, the Cross City service from Redditch to Lichfield via New Street.
Phase one of HS2 between London and Birmingham is scheduled to open in December 2026 with a second Y-shaped phase launching in two stages.
Phase 2a from the West Midlands to Crewe will open in 2027, followed by Phase 2b from Crewe to Manchester and Birmingham to Yorkshire via the East Midlands by 2033.
FirstGroup and Italian operator Trenitalia announced in January they would also jointly bid for the West Coast Partnership franchise.