A man and a woman will be charged with improper use of a communications network in relation to tweets to campaigner Caroline Criado-Perez, the Crown Prosecution Service (CPS) said.
However it would not be in the public interest to prosecute over messages allegedly sent to MP Stella Creasy, it added.
Twitter faced questions about the way it handled a sustained campaign of abuse against the two over the call for a woman's portrait to feature on a banknote.
Baljit Ubhey, chief crown prosecutor for CPS London, said: "Following early consultation with the police, the CPS has been asked to make a charging decision in respect of five suspects whom it is alleged sent offensive tweets to Stella Creasy MP and journalist and campaigner Caroline Criado-Perez.
"We reviewed these cases in accordance with the Code for Crown Prosecutors and guidelines issued by the Director of Public Prosecutions on prosecuting cases involving communications sent via social media.
"After careful consideration of all the available evidence, the CPS has today authorised the Metropolitan Police to charge two suspects in relation to messages allegedly sent to Caroline Criado-Perez.
"Isabella Sorley, 23, from Newcastle and John Nimmo, 25, from South Shields, have both been charged with improper use of a communications network under Section 127 of the Communications Act.
"We have also determined there is insufficient evidence to support a prosecution in respect of one suspect, whom it was alleged also sent offensive messages to Ms Criado-Perez, and have advised the police that no further action should be taken as the high threshold for prosecution has not been met.
"In respect of one other suspect, who allegedly sent offensive messages to Stella Creasy MP, we determined that although there was sufficient evidence that an offence had been committed under Section 127 of the Communications Act, it would not be in the public interest to prosecute, having applied the Director's guidelines and having particular regard to the young age and personal circumstances of the suspect.
"In relation to the fifth suspect, we have asked the police to carry out further investigation before a charging decision can be made.
"We have written to both Ms Creasy and Ms Criado-Perez to inform them of these decisions."
The two people charged will appear at Westminster Magistrates' Court on January 7.
Ms Criado-Perez said in a tweet: "Well that's pretty awesome. CPS informing press about charges ahead of me. About the level of victim-support I've grown to expect."
Ms Creasy, MP for Walthamstow, was said to have been targeted when she came to the defence of freelance journalist Ms Criado-Perez, who allegedly received an ''avalanche'' of abuse after leading a campaign for women to be featured on bank notes.
Scotland Yard gave details of the charge against Nimmo, of Moreland Road, South Shields. It said he had been charged with one offence, which was, between July 27 and July 30, sending by means of a public electronic communications network messages which were menacing in character, contrary to Section 127(1) (A) of the Communications Act 2003.
A 21-year-old man arrested on Sunday July 28 in the Manchester area in connection with an allegation of malicious communication had been informed he would face no further action.
A 32-year-old man arrested on Wednesday August 7 in Bristol, and a 27-year-old man arrested at an address in York on November 12, had been re-bailed to dates in January.
A 14 year old boy interviewed under caution on August 20 would face no further action.