Tuesday, January 22, 2013 at 11:36 AM 
The first lady wears a custom ivory wool-applique 3/4 sleeve coat and dress by Naeem Khan for the National Prayer Service this morning at the Washington National Cathedral. Note the jeweled neckline and trim. J.Crew Valentina patent pumps in Apricot Mist complete the neutral mix. So chic!
J.Crew, Naeem Khan Monday, January 21, 2013 at 11:36 AM 
On this very special day, the clothes are certainly more than just garments - they are an instant part of our social history. In 2009, Mrs. O wore an Isabel Toledo ensemble in a sunny lemongrass color that signaled newfound optimism. In 2012, the first lady's choice is symbolic in a different sense. Designed by Thom Browne, the 2012 recipient of the National Design Award in Fashion Design, this choice seems to honor the craft and artistry of fashion as a whole.
Per the Cooper-Hewitt, National Design Museum: "Thom Browne’s meticulous aesthetic is rooted in an American sensibility evocative of the late 1950s and early 1960s. Browne opened his doors in the fall of 2001, offering bespoke tailored clothing; he introduced ready-to-wear menswear in 2004 and womenswear in 2010."
From a White House official via the pool report: "The First Lady is wearing a navy Thom Browne coat and dress. The fabric was developed based on the style of man's silk tie. The belt and gloves she is wearing are from J.Crew and her earrings are designed by Cathy Waterman. She is also wearing Reed Krakoff boots. At the end of the Inaugural festivities, the outfit and accompanying accessories will go to the National Archives."
Update: Dr. Biden wears a Lela Rose silk bow coat per Eric Wilson of the New York Times.
Cathy Waterman, J.Crew, Reed Krakoff, Thom Browne Monday, January 21, 2013 at 9:31 AM 
The first lady wears a custom Thom Browne coat and dress, "both made of silk jacquard based on a necktie fabric," reports Eric Wilson of the New York Times.
The full scoop from a White House official via the press pool:
"The First Lady is wearing a navy Thom Browne coat and dress. The fabric was developed based on the style of a men's silk tie. The belt she is wearing is from J.Crew, the cardigan is designed by Reed Krakoff and her necklace is designed by Cathy Waterman. She is also wearing J.Crew shoes. At the end of the inauguration, the outfit and accompanying accessories will go to the National Archives.
Malia Obama is wearing a J.Crew ensemble. Sasha Obama is wearing a Kate Spade coat and dress."
Additional details to note: Marian Robinson wears hand carved, hand painted Lucite allegory flower earrings in black from Alexis Bittar.
This is not the first time that Mrs. O has worn Thom Browne. The first lady wore his lace overlay dress for the Democratic National Convention in September 2012, seen here. The designer is the recipient of the 2012 National Design Award in Fashion Design, celebrated with a White House luncheon ceremony hosted by the first lady.
Cathy Waterman, J.Crew, Kate Spade, Thom Browne Thursday, December 6, 2012 at 9:00 PM 
The first family attended the annual National Christmas Tree Lighting in Washington, D.C. this evening. For the occasion, Mrs. O dug deep into her closet, wearing a J.Crew blue tweed coat from January 2009, previously seen here. The first lady layered light trousers with a blue cardigan, an ivory scarf and a statement necklace. Joining in on the fun: Neil Patrick Harris and Rico Rodriguez!
Even better in video:
J.Crew Wednesday, September 5, 2012 at 7:17 AM 
The First Lady delivered her knock-out opening night speech of the Democratic National Convention wearing a custom-made Tracy Reese dress paired with J.Crew Everly suede pumps in rhubarb. For those curious about Mrs. O's nail color, People confirms the polish as Artistic Color Gloss Vogue in Grey Lilac. A fantastic ensemble from fingertip to toe!
Tracy Reese has been a staple designer in the First Lady's wardrobe during the first term, introduced when Mrs. O wore a pink lace dress by the designer for her February 2009 cover of People magazine, seen here. In celebration, Reese tweeted: "Thanks everyone for sharing this amazing moment! We are all so grateful and honored to have dressed Mrs. Obama for such a momentous speech!!"
Further Reading:
"Michelle Obama's Dress in High Definition" [New York Times]
"Michelle Obama: The Anti-Fashion Plate" [BuzzFeed]
"Designer Tracy Reese on Seeing Michelle Obama in Her Dress at the DNC" [Fashionista]
J.Crew, Tracy Reese