The highly-rated 21-year-old was widely linked to both Arsenal and Tottenham, with reports claiming he could move on loan.
But Morata, who has started just once in the league for Madrid this term, is to stay put and fight for his place.
Speaking after scoring in Real Madrid's 5-0 win over Real Betis on Sunday, Morata told reporters: "I have spoken with Carlo Ancelotti [Real coach] and the situation is clear.
"After many rumours about my future I can confirm that I am happy in Real.
"The club considers that I am necessary for the team and I have decided to stay until the end of season.
"I play for the best club in the world and I am obliged to improve my work. This is my mission. In the summer? I do not know, we will have to talk."