Surrey Police were working to decide whether Caroline Farrow had committed a criminal offence after a charity boss accused her of misgendering her daughter.
But on Thursday the force said: "The original allegation has subsequently been withdrawn and no further action will be taken in relation to this matter."
The incident in October came after Ms Farrow appeared on ITV's Good Morning Britain alongside Susie Green, whose daughter Jackie is transgender.
Ms Green, the founder of transgender support charity Mermaids, said she made the complaint because of the context surrounding the tweets, not solely because of the misgendering of her daughter.
'I couldn't let the constant referencing to herself as a victim stand'— Victoria Derbyshire (@VictoriaLIVE) March 20, 2019
Founder of trans charity Mermaids - Susie Green - reported tweets from journalist Caroline Farrow about her daughter who has transitioned, to police.
She explains why she withdrew the complaint yesterday. pic.twitter.com/t4Ic5Xl4cz
"She constantly refers to my daughter as a boy but that's not... the key issues in here weren't those," she told the BBC's Victoria Derbyshire programme.
"It was the really damaging things that she said about me and my actions that made me decide that this was an appropriate course of action."
On Tuesday, Catholic commentator Ms Farrow said that the police's move to investigate was an "outrage", adding: "I can't sleep I am so furious."
The force explained why officers investigated: "We have a duty of care to fully investigate all allegations which are reported to us. Once this investigation has been completed, a decision is made on the most appropriate course of action to take."
I am overwhelmed by media requests but I need to concentrate on a parent consultation about how my son is getting on in pre-school (he has a speech delay) and tonight my daughter is singing the solo in a choral society production of Vivaldi's Gloria & is a bag of nerves. ❤️— Caroline Farrow (@CF_Farrow) March 19, 2019
Ms Green said she had withdrawn her complaint partly to remove Ms Farrow's platform on the issue and to stop the "constant referencing of herself as a victim when in actual fact she's used her platform to deliberately go after myself and my daughter".
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