Although a married mum-of-two, she sent him love letters and smuggled a mobile phone top-up card out of the prison for him.
She even began house-hunting for them in Barton, planning their lives together for after his release.
The prison's deputy governor confronted Needham over rumours of her affair with the convicted criminal.
After Needham strenuously denied the allegations, labelling them "offensive", Gower was moved to Doncaster Prison.
However, the calls Gower made on an authorised prison phone were monitored closely by prison staff and Needham's secret relationship with him was uncovered.
Prosecutor Kathryn Goddard said: "The conversations between the defendant and Gower were of a personal nature.
"In these conversations, she referred to having hopes and plans for the two of them to have a life together when Gower completed his sentence.
"She spoke of going to view a house which she planned to buy for the two of them. She said she wished he was still in Hull and things were still the same between them."
After police were called in to investigate, Needham told them she had been flattered when Gower started flirting with her soon after he arrived on the prison wing where she worked.
Needham had failed to report he had a mobile phone and top-up card and on one occasion was caught smuggling his top-up card out of the prison to put credit on it.
Needham was then arrested as she collected a mobile phone during a meeting with his relatives in Scunthorpe.
A search of Gower's cell led to the discovery of a love letter from Needham.
The letter read: "Hey my super sexy gorgeous guy,How lazy of me typing this out for you but I got to see that house in Barton. It was really nice and you would have loved it I'm sure.
The area is really nice, I think we should definitely 100 per cent move there when you get out.
I know you will be happy there, I've got a really nice feeling about when you get out.
We only need to get June out of the way and then you've only got three years to go.
It is going really quickly, I will be here waiting for you no matter how fast it goes and no matter where you are.
I miss you so bad baby. I cannot wait for you to be out for us to do things together as a couple.
Needham had worked at the prison for six years and was a senior staff member in charge of the wing Gower was on.
Gower was jailed last June for an armed robbery and sent to Hull Prison for eight years.
Needham pleaded guilty to three counts of misconduct in a public office between February 9 and April 29.
The Honorary Recorder of Hull and the East Riding Judge Michael Mettyear has jailed her for eight months.
He said her conduct could have led to "manipulation and blackmail" of prison officers.
He told her: "The courts must send out the message that conduct like this is not acceptable and any prison officers tempted to behave in the way you did will be sent to prison.
"You have already lost a great deal. You have lost you employment and put financial and personal strain on your family.
"The risks of such a relationship are obvious but, because of your personal feelings, you went ahead regardless of the risks."
Her barrister Richard Thompson said: "This was behaviour which was out of character. She does not accept she had a physical relationship with him."
