The pair have posted a notice that they intend to get married there.
Earlier this week, the couple met with Superintendent Registrar Alison Cathcart, and the official notice - sometimes called banns - was made on Wednesday.
Nancy Shevell, Paul McCartney
The actual wedding date has not been announced, but they may tie the knot as early as September 30, and there has been speculation they will wed in October.
Paul McCartney and Nancy Shevell have been together since mid-2007.
The Beatles legend was married to the former Linda Eastman from 1969 until her death in 1998, then to Heather Mills in 2002 until their separation in 2006.
