Bayern Munich striker Kane missed his side's final two Bundesliga games with back issues he has been dealing with since before their Champions League semi-final loss to Real Madrid a fortnight ago.
However, England manager Southgate included the striker in his provisional squad for the June 14th - July 14th tournament.
"Kane is pretty much clear now. He is quite relaxed about it. I think a sensible decision was taken not to push for the last game there," Southgate said.
"Back problems can just happen, but it is not something we are concerned about at this moment in time. Our understanding of it is that it is something that is pretty much clear now."
Kane scored 44 goals in 45 appearances across all competitions in his first season at the German club, including four hat-tricks in the Bundesliga.
Yet he was unable to help Bayern win a trophy, the first time the German giants have failed to win silverware since 2012.
"It won't be nice for him and I am sure he will be aware of what people will say about that," Southgate said.
"But his love for this challenge and desire to make this work has never wavered and he is definitely looking forward to this tournament."
"He has delivered what we thought he would deliver in terms of goals in that league and I know the club are super happy with what he has done."
England play two friendlies - against Bosnia on June 3rd at St. James' Park and Iceland on June 7th at Wembley - before heading to the Euros, where they are in a group with Serbia, Denmark and Slovenia.