Operation Zygos was launched today to track down the suspected criminals, who are believed to be evading justice on the island, which has a large British expat community.
They include Paul Lockwood, 41, who is accused of raping a young girl from the age of six to 10, and Hasan Akarcay, who is wanted over the supply of £600,000 worth of diamorphine.
Martin Evans, 50, is also featured in the campaign for allegedly dealing cocaine, MDMA and Ecstasy in the UK. Costas Sampson is wanted by the Metropolitan Police in connection with the rape of a girl at a Greek club.
The operation is the first project to be launched jointly by Crimestoppers, the Serious Organised Crime Agency (Soca) and Cyprus Police.
Crimestoppers and Soca have previously worked together to track down 49 out of 65 suspects in Spain in 2006.
Lord Ashcroft, the Tory party donor and founder of Crimestoppers, said: "Operation Zygos is an example of the continuing impact Crimestoppers is having abroad in the fight against crime, and my hope is that we shall see more success in bringing some of the UK's most wanted fugitives to justice.
"While these suspected criminals will see Cyprus as a safe place to evade law enforcement, my belief is that with the help of the local public and ex-patriot community, these individuals will not be able to escape justice for much longer."
The agencies involved will alert the public in Cyprus - including Britons abroad - about the suspects, who are all the subjects of European Arrest Warrants.
SOCA deputy director, Martin Molloy, said: "Operation Zygos builds on SOCA's close relationship with Cyprus Police, working together to combat criminal threats to the public.
"Fugitives hiding overseas typically remain part of the criminal world, continuing to bring harm to communities locally and beyond. SOCA and our partners are determined to ensure life on the run is intolerable for them, and that they are returned to face justice in the UK."
Anyone with information from Cyprus can call a dedicated number, 8000 55 11, which will be answered in the UK by Crimestoppers' call agents and a translation service is available upon request.
They can also pass on information through a dedicated website, www.crimestoppers.org.cy. People in the UK can also pass on information anonymously via the Crimestoppers number 0800 555 111 or online at www.crimestoppers-uk.org.