A 23-year-old woman told journalist Caroline Criado-Perez that she had just been released from prison and would "happily do more time" to see her buried, a court was told.
John Nimmo, 25, and Isabella Sorley, 23, admitted a charge of sending the messages in July last year to the 29-year-old journalist
Westminster Magistrates' Court heard that Sorley sent a string of abusive tweets claiming that "rape" was the least of Criado-Perez's worries.
Nimmo, from Moreland Road, South Shields, Tyne and Wear, and Sorley, from Akenside House, Akenside Hill, Newcastle-upon-Tyne, sent the tweets after the Governor of the Bank of England Mark Carney revealed that Pride and Prejudice author Jane Austen would replace Charles Darwin as the face of the £10 note.
The announcement was hailed as a "brilliant day for women" by Criado-Perez who led a high profile campaign to ensure a female face on British banknotes in the wake of the Bank's announcement in April that social reformer Elizabeth Fry was to be dropped from the £5 note in favour of Winston Churchill.
Nimmo and Sorley were both charged with sending by means of a public electronic communications network messages which are menacing in character, contrary to Section 127(1) (A) of the Communications Act 2003.
The pair appeared at Westminster Magistrates’ Court.
The Crown Prosecution Service earlier admitted there was insufficient evidence to proceed with charges against a third individual who was also alleged to have sent “menacing” tweets.
Westminster Magistrates' Court heard that Criado-Perez was told to "f*** off and die you worthless piece of crap" and "go kill yourself" and "rape is the last of your worries" by Sorley in a series of tweets.
She also sent the message: "I've only just got out of prison and would happily do more time to see you berried!!(sic) #tenfeetunder not scared at what you will do!"
In a separate set of messages sent to Criado-Perez, John Nimmo, 25, told her "shut up bitch" and "Ya not that gd looking to rape u be fine" followed by "I will find you (smiley face)" and then the message "rape her nice ass", the court was told.
Nimmo also targeted Stella Creasy, the Labour MP for Walthamstow, with the message "The things I cud do to u (smiley face)", calling her "Dumb blond bitch."
Alison Morgan, prosecuting, said Criado-Perez had received abusive messages "of one type or another" from some 86 Twitter accounts including those accounts attributed to both Nimmo and Sorley.
"Caroline Criado-Perez has suffered life-changing psychological effects from the abuse which she received on Twitter," she told the court.
"In particular, the menacing nature of the tweets sent by both defendants caused her significant fear that they would find her and carry out their threats," she said.
She added that Creasy had also suffered a "substantial impact" as a result of "these events."
Morgan said "extreme language" used by Nimmo and Sorley had caused "substantial distress or fear".
She said Criado-Perez had described the tweets sent to her by Sorley as "horrifying and frightening and did scare me more than some of the others have".
The tweets sent by Nimmo were "menacing" to Criado-Perez in their reference to rape, his message that the "police will do nothing", the suggestion that she knew him and the threat that he would "come and find" her, she said.
"It is alleged that in July of 2013 both these defendants sent menacing messages via Twitter to the feminist campaigner Caroline Criado-Perez and also to Stella Creasy, the MP for Walthamstow," Morgan said, opening the case against the defendants.
"The background to these events was that prior to July of 2013 Caroline Criado-Perez led a campaign to ensure that a female figure appeared on a Bank of England note. Her campaign was conducted in a number of ways including using social media.
"It was supported by a number of high profile figures. The campaign was eventually successful in that on July 24 2013 the Bank of England announced that Jane Austen would appear on a bank note in the future."
She said following this announcement, Criado-Perez had appeared widely in the media and had been congratulated publicly by a number of high profile figures on Twitter, including Creasy, she said.
In the aftermath of this publicity, a "significant" number of offensive tweets were received into Criado-Perez's Twitter account from "many" Twitter users involving some 86 accounts including those attributed to Nimmo and Sorley, she said.
Nimmo was released on conditional bail, with Sorley, whose previous convictions include being drunk and disorderly on 21 occasions, remanded in custody.
The pair are due to be sentenced on 24 January at Westminster Magistrates' Court. Sorley was warned by District Judge Howard Riddle that it was "almost inevitable" that she would receive a jail sentence.
He warned Nimmo, described to the court as a "social recluse" who "rarely leaves his house", that "all options" as to sentencing remained open.
Nimmo was described in court as of "previous good character."
Morgan said Sorley had been arrested in October 2013 at her home in Newcastle.
In an interview with police she had admitted sending some of the tweets suggesting that she had been "off my face on drink" at the time, Morgan told the court.
Paul Kennedy, representing Nimmo, described him as a "somewhat sad individual" with "some level of learning difficulties" who had suffered bullying at school.
"He is a social recluse, that is exactly what he is really, he rarely leaves the house but to empty the bins," he said.
"He sits in the house 24/7, he has nothing to do, he claims benefits, he is a somewhat sad individual."
In a statement tweeted after the hearing, Criado-Perez thanked people for their support, but warned that Sorley and Nimmo represented a "small drop in the ocean" to the amount of abuse she received in July and August.
She said: "I am hugely relieved that these two defendants have pleaded guilty, meaning that there is no need for a trial and for the whole process to drag on longer – it has already dragged on for almost six months, with all the attendant anxiety you'd expect.
"This is not a joyful day; these two abusers reflect a small drop in the ocean, both in terms of the amount of abuse I received across July and August, but also in terms of the abuse that other women receive online – women who have little to no recourse to justice.
"However, I hope that for some people who are watching, this conviction will be a warning: online abuse is not consequence-free. I hope that some people watching will think twice before abusing someone else. There is not much else I can say given there are other cases still on-going."