Claire Darbyshire, 36, killed 67-year-old Brian at their home in Wykeham Green, Dagenham, east London, on 2 September last year.
Afterwards, she claimed they had made a suicide pact as his illness had become "intolerable".
But following an Old Bailey trial, a jury found Darbyshire guilty of murder.
Sentencing her, Recorder of London Nicholas Hilliard QC said he accepted that she believed it was an act of mercy.
He said the key to the case was that she failed to establish her father had agreed she would also kill herself in a suicide pact.
He said: "I accept your evidence that your father did raise the question of ending his own life and he wanted to do that and wanted your help to do so."
But he told her she had unlawfully killed her father behind "closed doors" and no defence to murder applied.
Darbyshire, who was born male but has lived her life as a female, has already spent five months on remand in a men's prison awaiting trial.
Widower Mr Darbyshire developed MS in 1995 and in 2014 the defendant took over as his sole carer.
Prosecutor Jonathan Rees QC told jurors that Mr Darbyshire, a retired Ford stock controller, had not expressed any suicidal thoughts or complained about being in pain to nurses who visited him.
Medical records revealed he had episodes of "bad temper and aggression", but had never tried to kill himself.
Darbyshire complained to a friend about having to look after him and appeared to be stressed.
After the killing she caught a train to the Dover area, having texted the district nurse to visit "asap".
On 3 September, Darbyshire approached a National Trust worker on cliffs for help and ended up with support services in Canterbury.
Five days later she mentioned the suicide pact for the first time. She said they had both taken an overdose on 1 September, which failed to work, before she suffocated her father.
On the morning of 10 September - eight days after the killing - police discovered Mr Darbyshire's body in his bed with a suit, teddy bear and various handwritten notes nearby.
Following her arrest, Darbyshire told police she had planned to hand herself in the next day and a signed account was found among her belongings.
In mitigation, Paul Keleher QC told the court that by 2015, Darbyshire and her father were "living a life which most people would regard as intolerable".
He also discussed a report about her time in custody, saying she had thought about self-harm when she first arrived in prison but "the kindness of strangers... brought her to the realisation that life was not desperate".
He added: "The prison will continue to support in terms of her ongoing transformation."
Det Insp Sarah McConnell from the Met Police's Homicide and Major Crime Command said:  "The reclusive lifestyle that Brian and Claire Darbyshire had lived for a number of years means it is difficult to fully understand their precise situation."
She said the unanimous verdict of murder "has been welcomed by the remaining family of Brian Darbyshire".

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A carer found guilty of murdering her MS-suffering father has been sentenced to life in prison with a minimum term of four years.
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