John Campbell, 59, was told he must spend at least 16 years behind bars for battering Robert Rose to death on Sanday in Orkney.
He had previously been found guilty of murdering the Yorkshireman, who began a relationship with Campbell's former flame after moving to the island for a "fresh start".
The body of 54-year-old Mr Rose, from Rotherham, was found in sand dunes last June after a two-week police hunt.
A trial at the High Court in Glasgow heard that the former construction worker had started seeing Campbell's ex-partner Margaret Johnston, 34.
Jealous Campbell, a monkey-keeper, murdered Mr Rose with the help of friend Stephen Crummack, 51, who was found guilty of culpable homicide.
Both were also convicted of defeating the ends of justice by concealing Mr Rose's body and driving his car to Loth Pier to make it look as though he had left the island on a ferry.
Lord Turnbull told Campbell: "You have been convicted of his murder, motivated it seems by your dislike of him and your reaction to his involvement with your former partner."
He said Campbell had lied to police and Mr Rose was a "kind and likeable" man who was "entirely harmless".
Campbell was sentenced to life in prison and told he must serve at least 16 years before being considered for parole.
Crummack was jailed for 11 years in total – 10 years for the culpable homicide and an additional year for the second charge.
Addressing Campbell, Lord Turnbull said: "Having heard all of the evidence at the trial, it was perfectly obvious that you lied to the police."