PC Nicholas Pool, of Cumbria Police, did not realise he was communicating online with an undercover officer.
A disciplinary hearing in Penrith dismissed the 29-year-old, of Newton Rigg, Penrith.
At Carlisle Crown Court last month, Pool admitted attempting to incite a girl to engage in sexual activity. He will be sentenced at a later date.
The hearing was chaired by Chief Constable Jerry Graham who said Pool's offences "undermined public confidence" and "brought discredit" on the force.
He added: "In light of all the evidence, it is clear PC Pool's moral compass is so distorted he is unfit to be a police officer and I have no hesitation in dismissing him."
The offences happened on 22 November and 11 and 12 December 2016 while Pool was off-duty.
He did not attend the hearing and is remanded in custody.
A police officer who attempted to meet a 12-year-old girl for sex has been sacked.