"When I [went] to LA the first time, we didn't know each other, only on the phone," began Cruz, 47. "I got here with a ticket to make a movie. I had my return ticket. So I was coming here for two months and I didn't know anyone here."
Despite the fact that they had previously never met in person, Cruz said Hayek picked her up from the airport and insisted she stay at her house instead of a hotel.
"She picked me up at the airport and she said, 'You're not going to the hotel. You're coming to my house because this is hard at the beginning. And you're gonna feel very lonely,'" the "Parallel Mothers" star said. "So she took me to her house."
And a friendship was born. "That's why now we're like sisters," Cruz continued. "I ended up also sleeping in her room because I was scared. And, you know, that's the way we met. And on top of that, in the middle of the night, she says that I was holding her hand because I was afraid. I don't know, I was dreaming."
"It was amazing," she added of Hayek, 55. "You know, that somebody that I really didn't know, only on the phone ... She told me, 'You are, whether you want [to] or not, you don't know me, but you're coming to my house. I'm not gonna leave you alone at the hotel.' I love her so much. From day one, she's been like that with me."
Meanwhile, also during the interview, Cruz chatted with DeGeneres about Hayek's owl, Kering, and shared why she was "blown away" when she met her.
"I love the owl," Cruz said. "When [Hayek] told me that she had one I was blown away because when I was little, my grandmother had a neighbor who had an owl and I was really scared of the owl, but always wanted to go and see her."
"[Hayek] invites us to feed the owl with these little rats and give[s] it to my daughter to give the rat to the owl, which is a little traumatic for her," she added with a laugh.
Cruz shares daughter Luna, 8, as well as son Leo, 10, with husband Javier Bardem.
See more from Cruz's appearance on "The Ellen DeGeneres Show" in the clip, above.