The couple reportedly arrived at LA's Cedars-Sinai Medical Centre on Thursday. Chris was seen pacing the corridors of the hospital, while security guards are allegedly guarding the door of Elsa's suite. No names or genders have been revealed.
Husband and wife announced the news of their second pregnancy in November, and confirmed in January that they were expecting twins. The new arrivals are siblings for the couple's daughter India, who will be two in May.
Fast & Furious 6 star Elsa was last seen on the red carpet at the Oscars, looking heavily pregnant as she supported her husband Chris in his presenting duties.
Speaking exclusively to HELLO!'s sister publication HOLA!, the blonde beauty said that she was sure the twins would come early.
Elsa also revealed that she chose not to find out the sex before because "I didn't want to obsess over it". When she began getting too big to bend down comfortably, Thor actor Chris stepped up his efforts in helping around the home.
Apart from tidying up, which Elsa says he's always done, the 30-year-old Aussie star took the lion's share of the work with their toddler, taking India to ride her bike and organising bathtime.
Luckily, the parents will have plenty of help in looking after the new arrivals. Ahead of the birth, both grandmothers decamped to Malibu, where the couple recently bought their dream house by the beach.
In the run up Elsa also had a star-studded baby shower, organised down to the last detail by two friends.
"I'm not very good at organising events," laughed the 37-year-old yummy mum. "Even at our wedding there weren't that many people. I prefer things that are more informal and Chris is the same. We love having people over, but it's all very spur of the moment."
The Spanish actress - who previously dated Adrien Brody and Olivier Martinez - couldn't be happier with her personal life at present.
Elsa and Chris met through their management companies in early 2010 and married later that year at Christmas.
Of their bond, she says: "When I began seeing Chris I thought: 'This is what it means to have a relaxed relationship. Without any problems, without fighting'.
"I love his personality and the fact that he's a great father. That's what makes a woman really love a man..... Seeing him with India and knowing how much he wanted to have a family with me is what most attracted me to him."