If you want to receive a letter from President Obama and his wife expressing congratulations to you on your big day, then all you have to do is send him a wedding  invite. Here are three ways to request a greeting:
Address the envelope to the following:
Honorable Barack Obama and Mrs. Obama
The White House
Attn: Greetings Office
1600 Pennsylvania Ave. NW
Washington DC 20500
Or you can also email a request by filling out and submitting an online form through this link , which is actually their preferred method.
Call the White House switchboard 1-202-456-1414 and ask for the greetings department.
Although there is a very slim chance that the president will attend the wedding, you will at least, most likely, receive a letter of congratulations. It'll be a nice memento to keep in your wedding scrapbook or to frame and display at home.
Source: Etsy user casalastudio