Nimmo, 28, who was jailed for eight weeks in 2014 for sending abusive messages to Labour MP Stella Creasy and feminist campaigner Caroline Criado-Perez, has been remanded in custody until February 10 when he will be sentenced.
In a separate incident he admitted sending emails to an anti-hate group in which he threatened to blow up a mosque.
Ms Berger, the former shadow minister for mental health, said the messages had caused her “great fear and anguish”.
She said the tweets had left her in a state of “huge distress” and “it caused me to feel physically sick being threatened in such a way”.
“I was extremely concerned for my safety and I felt completely under threat. I had previously received anti-Semitic messages and threats but the reference to Jo Cox was terrifying,” she said.
“The biggest concern was not knowing who this was, for all I knew the offender could have resided next door to me.”