Morata, who has seven goals in 22 Serie A appearances this term for the Italian champions, was included in coach Vicente del Bosque's squad for Friday's Euro 2016 qualifier at home to Ukraine and a friendly away to Netherlands four days later.
Costa has been forced to withdraw with a hamstring injury and Morata will compete for a place up front with the likes of Barcelona's Pedro, Malaga's Juanmi and possibly Cesc Fabregas, who plays in midfield for Chelsea but has often been drafted in as an auxiliary striker for his country.
Morata, 22, joined Juve from Real Madrid in the close season after coming through the European champions' youth ranks but then finding his playing time in the first team limited.
He has a similar profile to Costa. Strong in the air and dangerous when running at defences, he can also shoot from distance.
Morata said his experience playing for Spain at junior level, including winning the European under-21 title in 2013, would stand him in good stead in the senior squad.
"I will have to work very hard to get any playing time," he told a news conference at Spain's training base outside Madrid on Tuesday.
"There are a lot of people who are in great shape and it will be tough to get into the side but I will give my all," he added.
"I am playing well for my team. I am very happy with my season and I am coming here to enjoy myself, to try to perform and to learn."
With four matches played, Spain are second in Euro 2016 qualification Group C on nine points, three behind leaders Slovakia, who beat them 2-1 in Zilina in October, and level with Ukraine.
(Writing by Iain Rogers, editing by Pritha Sarkar)
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