The couple - who already have daughter India Rose, 22 months - welcomed the boys into the world earlier this month and now the Spanish actress has revealed what they have called their two sons.
Posting a picture of the twins' feet on her Instagram page, she wrote in Spanish: "You are home! Tristan and Sasha came to this world on March 18 just after the full moon. Complete happiness."
Elsa has also advised new parents to treasure every minute with their babies.
Writing in a blog post for Spain's Glamour magazine, she said: "Enjoy every second with your baby because it is the most wonderful thing of the world."
Proud father Chris, 30, previously gushed about family life and admitted he is happiest when he is with his wife and daughter.
He said: "Being a father is certainly a task. But the best one that I could ever ask for. Being home, being with the family, that's what it's about ... It makes me much more relaxed with work, because I have something that is far more important to me now."
The actor married Elsa, 37, in 2010 after a whirlwind romance.