Ahead of La Roja's opener in Toulouse on Monday, the 23-year-old forward is confident of making Vincente del Bosque's starting XI.
"I feel very good," said Morata. "The discomfort has passed and I did not play in the last friendly [a 1-0 defeat to Georgia] in order to get better.
"If the coach decides, then I'll be ready to play against the Czech Republic."
Del Bosque has five strikers in contention for the game, with Aritz Aduriz, Lucas Vazquez, Pedro and Nolito all vying for what is likely to be a lone striker role in the team.
Morata said: "We have a selection of very good strikers. Some did not come [to the tournament] and I am proud to lead the team.
"It is a great responsibility, which generates a lot of pressure and I am ready to be the striker of Spain."
He added: "It is very important to me, the Euros. It will be my first European Championship and it is a dream to play in the Spanish national team."