Terry was among those who needed to be checked after suffering a "tight hamstring" in Saturday's friendly win over Belgium.
However, the FA said all players trained in their final session at Arsenal's London Colney complex on Wednesday morning and will make the two-hour flight to England's tournament base in Krakow.
After losing four players to injury already, and becoming embroiled in a row over Rio Ferdinand's omission, manager Roy Hodgson will be relieved not to suffer any more unwanted setbacks.
England were putting on a unified front before their departure from The Grove hotel in Hertfordshire, with players and officials posing for final photographs, resplendent in their new suits.
On their way to Luton, England were also due to call in at the car plant of main sponsors Vauxhall, where they were expected to meet 200 members of staff before making the short journey to the airport.
Having taken a conscious decision to base themselves in a city centre location in Krakow, it was yet to be established whether there would be an FA presence in the city on Wednesday evening.
However, a ceremony was going to be conducted at Krakow airport, organised by UEFA, which would confirm England's arrival, following that of Netherlands and Italy, who have also chosen to base themselves in the same area.