Officers said 84 incidents of rape or attempted rape were reported from April 2014, compared to 35 the previous year.
Posters offering support to victims have been released urging more men to come forward in a new campaign led by Greater Manchester Police (GMP) and abuse charity, Survivors Manchester.
A police spokesman said they believed a large number of crimes go "unreported".
Sexual assault reports have also risen from 69 to 93 over the same period.
Duncan Craig, from the charity, said: "We need to work together to break the silence that surrounds the rape and sexual assault of men, so those affected can get the support they deserve."
The posters feature "real men rather than models" after an online appeal for volunteers, he added.
Reports of male rape in Greater Manchester have more than doubled in the last 12 months, police said.