A judge said Cody Ackland carried out a “prolonged, savage and merciless attack” on the student last November.
He told the 24-year-old killer his crime was “utterly motiveless” and he had caused “outrage and fear in this part of the country”.
Ackland nodded as his sentence was passed at Plymouth Crown Court on Thursday.
As he left the dock, McLeod’s brother shouted: “You’re a dead man.”
The 18-year-old was last seen at a bus stop in Leigham, in Plymouth, last November when she was heading out to meet friends.
This is where Ackland snatched her, struck her twice to the head with a claw hammer and bundled her into his car.
He would later bludgeon her to death in a remote car park on Dartmoor.
The 24-year-old then burnt her handbag and loaded her bloodied body into his boot and drove 30 miles back towards Plymouth to Bovisand, around seven miles from her home, where he stripped her naked and left her in undergrowth.
He later threw away her clothes in an allotment before spending the next 48 hours socialising with friends.
Three days later, Ackland turned himself in and confessed, telling detectives where he had dumped her body.
He was unknown to police at the time.
The court heard Ackland told detectives during his interview he had “never met her before and did not know her name”.
He claimed he targeted Ms McLeod as she “resembled his ex”.
He told police: “I got myself wound up and needed to go out.” He said he was just watching television and “needed to get out and do something”.
Ackland described striking her 12 times to the head with a hammer to the head and face, but she was still breathing.
He said in interview: “It’s not funny but she started to make a noise and I thought ‘f****** hell, wow, I mean hats off to her’.”
He added that he had also trodden on her neck to suffocate her.
On Thursday, Judge Robert Linford told Ackland: “The evidence discloses that you had a worrying and disturbing interest in murders and serial killers.
“Images were recovered from your mobile telephone, which included photographs of bodies, post-mortems, human remains, injuries to people and serial killers.
“This macabre interest is indicative, suggests your advocate, of no more than morbid fascination.
“But I’m satisfied so that I’m sure that based upon the extensive internet searches that you carried out, that your interest in this material went beyond morbid fascination.”
Sentencing Ackland to a minimum 31 years in jail, the judge said there were “seriously aggravating features” of the murder.
He said this included the “mental and physical suffering” inflicted on McLeod, who faced four murder attempts: when Ackland hit her with a hammer at the bus stop, strangled her in the car, struck her repeatedly with a hammer on a moor, and finally stood on her throat.
“This was a prolonged and awful ordeal for this poor person,” the judge said.
Plymouth Crown Court heard how Ackland, who was a guitarist with local indie band Rakuda, led a “double life”.
“He held such an unhealthy fascination and desire to imitate serial killers. His fascination was to become an unimaginable wicked reality for Bobbi-Anne,” Richard Posner, prosecuting, said.
The court heard Ackland looked for information on Ted Bundy and Fred West in the week before killing Ms McLeod and also looked up Richard Chase and the Vampire of Sacramento two days before.
Mr Posner said: “His interest in the macabre presents as deep-rooted; a fascination with death, murder and murderers and the means to commit murder.”
Ray Tully QC, who was defending Ackland, had told the court his client’s obsession with images of murder victims had to be viewed through the “prism” of his mental health struggles.
He said Ackland described it as “self-medicating” in the sense that “if he can shock himself he might shock himself out of what he felt he had become capable of doing”.
Judge Linton told Ackland at his sentencing on Thursday: “I cannot be satisfied to the required standard that you drove into Plymouth on the evening of the 20th of November with a settled intention to kill that night. But it was only going to be a matter of time.
“And, sadly and tragically for Bobbi McLeod, that time was, as it turned out, going to be that night.”
Ian Wilkinson, senior crown prosecutor for the Crown Prosecution Service in the southwest of England, said: “Bobbi-Anne was just 18 years old when her life was taken away in the most cruel and shocking manner.
“As this case reaches its end, our thoughts are very much with Bobbi-Anne’s family as they continue to live with what Cody Ackland did.”
In a statement released by Devon and Cornwall Police after the sentencing, McLeod’s family said they wanted Ackland to know “he has taken away our world”.
“We will never see her beautiful face or hear her laugh, see her get married or have the children she so wanted. So many everyday things have been taken away. Her not being here is still unimaginable,” they said.
“Our lives have changed forever. We have not been able to say goodbye to Bobbi-Anne and we can only imagine the things he did to her – the thoughts are continually going around in our minds.”