A tender for the contract, worth £150,000, was called in April and includes raising awareness of the museum via a campaign that generates "affection and advocacy" among Londoners, the Museum of London said. It runs until December next year.
Andrew Marcus, head of communications at the museum, said: "As the Museum of London looks towards a future in West Smithfield, our communications will become ever more sophisticated so that people get to know that the Museum of London is the Museum of Londoners.
"Pagefield's appointment marks the next step in the evolution of this campaign, which spans the full marketing mix. The campaign aims to significantly raise our profile ready for when the new Museum of London opens in 2022."
Earlier this year, Museum of London also awarded Pagefield a separate contract to deliver its City Now City Future campaign, which runs until April 2018. That campaign is designed to help reposition the museum ahead of its relocation.
Museum of London also works with London Communications Agency around its planning permission for the new site. Pagefield and LCA will be working together, with the museum's in-house team, on different aspects of the new museum project, Marcus said.
Museum of London, which is designed to tell the story of the city and its inhabitants, has sites in London Docklands and Hackney as well as its main premises in Barbican.