Alan Hagan, 48, of Liverpool, was convicted over his dealings with News of the World reporter Lucy Panton in 2008 while he worked at Ashworth Hospital, Merseyside.
He denied misconduct in a public office but was convicted at the Old Bailey.
Moors Murderer Brady has been at Ashworth for 30 years.
Sentencing, judge Mark Lucraft QC rejected a call from his lawyer for a suspended sentence, saying only immediate custody was appropriate.
He said: "At Ashworth, where staff deal with some of the most vulnerable and dangerous people, the confidentiality of patients should be safeguarded."
The judge said Brady "took against staff and became uncommunicative when he thought information was being leaked to the paper."
The court heard Hagan, of Galston Close, Liverpool, was paid Â£1,000 for a story headlined "Suicide Brady hid pills in his sock" in February 2008, shortly after he first made contact with Ms Panton.
He wanted to take revenge on bosses at the psychiatric hospital for his treatment as an employee, and discussed payment of Â£50,000 for the images.
Even though he did manage to smuggle a camera into the hospital, the resulting pictures were not good enough quality and they were not published.
Brady, 77, who has been a patient at Ashworth since 1985, tortured and murdered five children with Myra Hindley, who died in prison in 2002.
He was jailed for three murders in 1966. The pair later confessed to another two murders.
Earlier in the mitigation, Michael Duck QC said Hagan was a man of "positive good character" who had not instigated the plan to get pictures of Brady or actively sought payment.
A security officer has been jailed for 20 months after smuggling a camera into a high security hospital to try and sell photos of Ian Brady.