The Juventus forward missed the 1-0 home defeat by Georgia on Tuesday with a thigh injury but will be available for Spain's Group D opener against Czech Republic in Toulouse on Monday.
"I feel very well," Morata told a news conference in Ile de Re, Spain's headquarters during Euro 2016. "The pain has passed and I didn't play the last friendly in order to arrive better.
"If the coach decides, I will be ready to play against the Czech Republic."
Morata scored seven goals and set up seven more to help Juventus clinch the Serie A title.
Spain coach Vicente del Bosque can also call on Aritz Aduriz and Nolito.
Aduriz, 35, scored 33 goals in 44 appearances in all competitions for Athletic Bilbao last season, while Nolito had an outstanding campaign with Celta Vigo.
Nolito has played in three friendlies and scored four goals for Spain.
"This team has very good strikers," said Morata, a former Real Madrid player. "Some have not been selected and, for me, it's a great pride to be a striker for Spain.
"It's a huge responsibility, it generates a lot of pressure but I'm prepared to be the striker for Spain.
SPECTACULAR ATMOSPHERE
Spain go into the tournament as twice defending champions but on the back of their first defeat since March 2015. Morata says the setback against Georgia has not affected the team.
"The atmosphere is spectacular and we just have to focus and not think of whether or not we are favourites," he said. "We can have a good tournament.
"But there are very good teams that are dangerous and any side can win the trophy."
Morata, who won the European Under-19 Championship in 2011, and was the tournament's highest scorer with six goals, made his senior debut in November 2014 and has scored three goals in nine games.
"Many youngsters that are here have been champions," Morata said. "There is a good group between youth and veterans.
Morata is reportedly a target of top English Premier League clubs in the transfer window but has taken it all in his stride.
"I'm calm," he said. "I feel right at home at Juve. I know this is a very important European Championship for me. It's my first European tournament and it's a dream to play for Spain."
(Writing by Cindy Garcia; Editing by Ken Ferris)
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