The couple said they were "delighted" after a caesarean section delivery in Madrid at 1040 local time (0940 GMT) on Sunday. The baby weighed 7lb (3.2kg).
The Real Madrid and England star said: "He's gorgeous, healthy and his mum is very good so we're a very happy family. He's got Victoria's lips and nose."
Cruz means cross in Spanish. First son Brooklyn is now five and Romeo is two.
David said the couple had been advised to have the baby delivered a week early but mother and baby were "really well".
An earlier statement said: "David and Victoria Beckham are delighted to announce the birth of their baby boy Cruz Beckham, born today at 10.40am at the Hospital Ruber Internacional, Madrid."
Dr Vidal Pelaez, head of the obstetrics and gynaecology department at the hospital, said: "Mother and child are in perfect health. Medical intervention lasted 30 minutes with no complications whatsoever."
Cruz is a common surname in Spain and South America, but is an unusual first name, according to Lola Oria, Spanish language tutor at Oxford University.
She said Cruz is actually an old-fashioned girl's name, adding: "It is quite a strange thing to do to a little boy."
But Cruz Bustamante, who stood against Arnold Schwarzenegger's in the election to be governor of California, is one example of a man named Cruz.
Bookmakers William Hill are offering odds of 100/1 that Cruz Beckham will play for England one day and 1,000/1 that all three boys will get into the England team.
Victoria Beckham is thought to want to pursue a fashion career
News of the pregnancy came months after high-profile reports that David had an affair and rumours that their marriage was in trouble. But the footballer described the stories as "ludicrous".
The couple met in 1997 and married in a lavish ceremony at Luttrellstown Castle in Ireland four months after Brooklyn's birth in 1999.
Victoria had a string of solo hits after the Spice Girls split, most recently reaching number three in the UK with This Groove/Let Your Head Go in January 2004.
But in November, she reportedly said she was abandoning her music career to concentrate on fashion designing and motherhood.
Who cares what they call the little chap? He will want for nothing, but will always NEED the love of his family. Good luck to the Becks, I say.
Shirley Wallis, Newport, Shropshire
Let's face it, the name was always going to be scrutinised - whatever it had been! It's unusual, but could have been a lot worse! Good luck to them!
Lizzie, Suffolk, England
Cruz is a fantastic name. I love it. I just wish the Beckham family all the best.
Who cares if it's usually a girl's name? You get boys called Tracy, Shirley, Lindsay, all traditionally 'girl's names'. And you get girls called Teri, Robin, Charlie, for example. They can call their child whatever they want. And good on them for having the courage to choose something unusual.
Vikki, London, UK
I think that David and Victoria choose ridiculous Christian names for their children just for the publicity it gives them. They do not spare a thought for their poor kids who have to grow up with silly names. They are not the first! David Bowie saddled his son with the ridiculous name "Zowie" but when he became an adult he changed his name to Joe.
Diane Britton, Salford, England
The media is making too big of a deal of the chosen name, which isn't just a girls name, it's also a boys name and a common surname as well. Besides it's better than naming a child after a fruit or vegetable! Let the Beckhams name their children what they want and just leave them alone.
Wishing them all the best in life.
Diana Kambona, Malawi, Southern Africa
I'm really glad that the Beckhams have been blessed with another child and I wish them all the best in life. I think people should just respect the name they have chosen and just accept it for once!!
Rutendo Hatendi, Harare, Zimbabwe
With a name like that, the poor lad will be Cruz-ing for a bruising at school. Unlike his dad, he'll have to learn how to control (Cruz control of course) his temper at an early age - otherwise he'll get Cruz-ified...
I wish them all the very best. It is an unusual name, one I've seen as a surname but not a first name. I've heard of far worse from everyday mums and dads, it's not just celebs who choose strange names for their children. To be honest the baby was never going to have a 'normal' name anyway.
Jo, Bristol, England
Cruz is a nice name, but big deal! They had another baby and gave it an unusual name, what celebrity doesn't these days?
Jenna Aspinall, Warrington, England
Cruz is a lovely name for their son. Unusual names are now more popular than ever. I am glad to hear mother and baby are doing well.
Hayley Fleet, Liverpool, Merseyside
The poor little guy will be picked on at school for having a girl's name! They may have well just called him Mary or Jane.
Phil C, London, UK
Cruz is a very common first name in El Salvador for both boys and girls.
Anne Griffin, Arambala El Salvador
I think it is great news and a good name too. Love and best wishes to the whole family.
Elizabeth Nickson, Sandbach ,UK
I'm a big fan of the Beckhams and I think their fab! They are such a nice couple and deserve the best. Brooklyn and Romeo are real nice names, and I think Cruz is really cool and unique. All three names couldn't get any better!
Nazia Sheikh, Southall, London
I am only surprised they didn't name him "Real". This word translated from Spanish to English means - Royal. Enough said.
Paul Dawes, The Netherlands
Having a ridiculous name won't matter to the boy as when he goes to school it won't be with the ordinary kids. He will no doubt go to a private school, among all the other Fifi Trixibelles, Moon Units, Romeos, and Brooklyns etc. So he won't stand out.
Allan Jamieson, East Kilbride, Scotland
Who cares what they call their baby! I think it's about time the Beckhams were left alone to get on with things.