Suri is the first child for Holmes, while Tom Cruise, 43, has two adopted children from his marriage to Nicole Kidman.
Tom Cruise and Katie Holmes have been engaged since June 2005 and they plan to marry in late summer or early autumn.
Spokesman for the pair Paul Bloch said in a statement that the couple "joyously welcomed" the arrival of their daughter.
The baby's name, Suri, comes from Hebrew, meaning "princess" or in Persian, meaning "red rose", the statement said.
The baby weighed 3.4 kg (7lb 7 oz) and measured 50.8 cm (20 inches), Mr Bloch added.
No details were given about the birth itself.
