On 18 March 2014, Morata scored his first goal in the UEFA Champions League, the third goal in a 3–1 win over Schalke 04 at the Santiago Bernabéu in the round of 16. On 17 May, in the last game of the league campaign, he scored two late goals against Espanyol to help Real to a 3–1 home win, and finish with eight goals in the competition. He also featured in the club's victory in the UEFA Champions League Final against Atlético Madrid, playing the last ten minutes of regular time and extra time after replacing Benzema.
On 19 July 2014, Juventus announced that they had reached an agreement for the fee of €20 million for the transfer of Morata, who signed a five-year deal, with Real Madrid having the option to buy him back in the future. He made his debut in Serie A on 13 September, replacing Fernando Llorente for the final minute of a 2–0 home win against Udinese; two weeks later he again came on in place of his compatriot, and headed his first goal for his new club as they won 3–0 at Atalanta.
On 5 October 2014, in a 3–2 home win against Roma, Morata came on as a substitute and was sent off for a foul on Kostas Manolas, who was ordered off for retaliating. On 9 November he scored twice in a 7–0 home demolition of Parma, with Llorente – whom he replaced after 71 minutes – adding a further two. Morata came on for the final ten minutes of the Supercoppa Italiana against Napoli in Doha, Qatar on 22 December, and scored in the penalty shoot-out which Juventus lost 5–6.
On 7 November 2014, Morata was called up to manager Vicente del Bosque's senior squad for matches against Belarus and Germany. He made his debut against Belarus on the 15th, replacing Isco for the last ten minutes of a 3–0 win in Huelva for the UEFA Euro 2016 qualifiers. In the same competition, on 27 March 2015, he scored his first senior international goal, the only goal in a victory over Ukraine in Seville.
In March 2014, Morata shaved off all of his hair in solidarity with sick children, saying "kids with cancer wanted to have my haircut but they couldn't, so I gave myself theirs".