The agency has been appointed to carry out a press office function and awareness-raising brief to help drive sales to the museum's online shop, which is to be relaunched this month.
The agency has also been called on to increase consumer awareness of its merchandise generally.
A media relations campaign will form the backbone of the strategy, with particular focus on the Christmas market, as well as supporting tie-ins with forthcoming exhibitions.
The agency, which was set up by Hilary Frohlich, wife of Ogilvy PR’s UK MD Michael, also holds the retail PR accounts for the Science Museum, National Media Museum and National Railway Museum.
Andrew Marcus, press and PR manager, Museum of London, said: 'Our vision is to create a revitalised, world-class museum.
'One of the ways we will achieve this vision is to act more commercially as an organisation. It is the perfect time to be working with Neat PR to increase awareness of our superb retail offer and ultimately generate sales.'
Frohlich said: ‘The Museum of London shop is full of exciting surprises and we cannot wait to let the media and the public know about them.’