The child arrived safely this weekend, according to the actress's spokeswoman Emily Yomtobian who could neither confirm nor deny whether his passage into the world had been hastened through a Caesarean section. Ms Yomtobian would say only that he was healthy, adding: "Mum and baby are both doing well. I'm sure they are ecstatic."
The name has been one of the most eagerly awaited announcements in the world of showbusiness, not least since the couple called their first-born daughter Apple two years ago. Naming their second born after the Jewish prophet however appears less surprising in the context of Paltrow's family history.
While her mother was a Quaker, the star's father, the film director Bruce Paltrow, was a prominent Jewish American. He in turn was a direct descendant of David HaLevi Segal, the 17th century patriarch from Krakow, part of the mighty Paltrowich dynasty which gave the world a further 33 rabbis.
As for the importance of the name to Martin, Moses was the title of a song he wrote for his wife shortly before their low-key wedding in California in 2003. The previously unreleased track was included on the his Live 2003 album, recorded in Sydney.
The lyrics include the words: "Like Moses has power over sea so you've got power over me ... You're a refuge, somewhere I can go. You're air that, air that I can breathe, 'cause you're my golden opportunity." Martin told fans it was the song he most enjoyed performing.
The naming of the couple's first child prompted considerable amusement in the media and provoked comparisons with stars such as Frank Zappa and David Bowie, who called their children Moon Unit and Zowie respectively. For the down-to-earth Martins, the truth was altogether more prosaic. It was eventually revealed that the girl, Apple Blythe Alison Martin, was named after the daughter of the singer's new agent, Marty Diamond. Paltrow told Oprah Winfrey: "It sounded so sweet and it conjured such a lovely picture for me - you know, apples are so sweet and they're wholesome and it's biblical - and I just thought it sounded so lovely and clean."
The couple are famous for their squeaky-clean lifestyle. Strict vegans, espousing macrobiotic foods and eschewing the traditional drug and drink excesses of their trades, their straight stance has earned some harsh press coverage. Martin has been called everything from "ultra nerd" to the leading light of the "gloom rock" movement. His brand of liberal politics, association with the fairtrade movement and high profile at last year's Live8 project has led to accusations that he takes himself somewhat too seriously. Paltrow is also no stranger to politics. She supported the presidential election campaign of Senator John Kerry in 2004 and gave money to Emily's List, a network of pro-choice Democratic women.
The Oscar-winning star's former boyfriend, Brad Pitt is also expecting a child with his partner Angelina Jolie.
In what promises to complete a hat trick of A-list births, Tom Cruise and his fiancée Katie Holmes are also due.
Odd sounding offspring
* Moon Unit, daughter of Frank and Gail Zappa. Her siblings' names were hardly more conventional: Ahmet, Diva and Dweezil
* Elijah Bob Patricius Guggi Q Hewson, son of Bono and Ali Hewson
* Poppy Honey and Daisy Boo, daughters of Jamie and Jools Oliver
* Zowie, eldest son of David Bowie and his first wife Angie
* Rolan Bolan, son of Marc Bolan and Gloria Jones
* Fifi Trixibelle, Peaches Honeyblossom and Pixie, daughters of Bob Geldof and Paula Yates. Their half-sister's name is equally as exotic: Heavenly Hiraani Tiger Lily - daughter of Ms Yates and Michael Hutchence, the late INXS singer
* Dandelion Pallenberg, daughter of Anita Pallenberg and Keith Richards
* Tallulah Willis, daughter of Bruce Willis and Demi Moore