Both players are in Luis Enrique's first Spain squad this week.
Morata said: "It's clear that he deserved it, I'm very happy for him.
"I'm his friend, he's one of the most important players for Chelsea, today I told him how weird to see him around here."
He added: "I wish I could play someday with him, there are a lot of people who cannot imagine what friends we are.
"Five minutes after the list for Russia, when I was very upset, I wrote to him and Iago (Aspas): let's see if you can bring the World Cup home."