The agency has been briefed to put the market back on the map following the completion of its four-year restoration.
The broad-ranging account was won following a three-way pitch.
Redhead will promote the market to tourists and travellers to London, market traders, local residents and businesses that may want to use the new events facilities.
It will also highlight its quirky fashion credentials. The market recently won 'Best Fashion Market' in the Time Out shopping awards.
The agency will also handle media relations for a range of events taking place this year.
RedheadPR founder and MD Sara Tye will lead the account.