The 35-year-old actress gave birth in a hospital earlier this week, just weeks after being seen showing off her huge bump at a Hollywood showbiz event, reported Daily Mirror.
The sex of the children are not yet known.
They are Saldana's first babies with the artist husband.
"Zoe and Marco are delighted, Zoe has been ready to drop for some time and they are both ecstatic to be meeting the twins.
"This a dream come true for both of them, they are absolutely delighted. They have been looking forward this day for the last nine months. "Both want a big family so this is the start," a close friend of Saldana said.