A judge at Birmingham Crown Court told Costco store manager Roger Cooper, 41, and ex-soldier David Cooper, 39,  they must serve at least 30 years for killing  34-year-old Sameena Imam.
Ms Imam had been having a two-year affair with Roger Cooper and issued him with an ultimatum to leave his partner.
Her body was discovered buried in an allotment in Leicester in January.
An eight-week trial heard Roger Cooper spent at least a month plotting to kill Ms Imam - one of his three lovers - to prevent her exposing their affair.
The men bought poisonous metals, identified a shallow grave and communicated in text messages written in a Star Wars-based code before killing Ms Imam.
Ms Imam is believed to have been overpowered on a sofa at David Cooper's home in Leicester after being driven to the property from Coventry by his brother.
She was reported missing by family members in Essex after failing to return home for Christmas, sparking a major police inquiry.
Jailing the pair, Judge Patrick Thomas QC told the siblings: "The use of a poison in a case such as this demonstrates a cold-blooded intention to kill, regardless of the consequences.
"You worked together, hand in glove, in planning and carrying out the murder of a joyful and bubbly young woman, brutally betrayed by a man she loved and his brother."
After a jury returned unanimous guilty verdicts on Tuesday, the detective leading the murder hunt described the killing as "the most callous offence" she had ever investigated.
"Most murders that occur are spontaneous events driven by anger or jealousy, whereas in this case what we uncovered was weeks and weeks of planning to kill Sameena, numerous attempts on her life and a really unusual cause of death," said Det Chf Insp Caroline Marsh.
After the conviction, Ms Imam's family said nothing could have prepared them for discovering she had been murdered.
In a statement, her father Imam Din said: "As a family we are absolutely devastated at the loss of Sameena.
"It is hard for us to even imagine that an innocent, kind, beautiful girl could be murdered, let alone our daughter.
"We are still in shock and we are all missing Sameena in so many different ways."
Two brothers who used chloroform to murder a cash-and-carry manager from Cardiff have been jailed for life.