Sam Spaven drove his Audi into Richard Pencott, 44, as he rode home from work in Harworth, Nottinghamshire, in June.
Nottingham Crown Court heard Spaven had become abusive to his ex-partner when he learned she was seeing Mr Pencott.
The 27-year-old, of Bircotes, Nottinghamshire, pleaded guilty on the first day of his trial and must serve at least 25 years behind bars.
Spaven has a son with his former partner Amy Sherwood but the court was told they split up in April.
He became angry after finding out she had been seeing Mr Pencott, a former work colleague of his.
On visiting her home, he told Ms Sherwood "I'm going to chew your face off'" before threatening to kill her and Mr Pencott, Michael Evans, prosecuting, said.
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Spaven returned the next day and was told to leave around the time Mr Pencott was finishing his shift.
He then posted on Facebook: "Richard Pencott and Amy Sherwood have broken me and my family apart and my boy" before driving to "exact his revenge", Mr Evans said.
He mounted the pavement in Blyth Road and drove into Mr Pencott's bicycle, which landed the other side of a 10-foot fence.
The father-of-two died almost instantly from head and chest injuries.
Spaven then drove to work at a gym in Rotherham, where he was arrested.
Witnesses reported seeing damage to his car's windscreen and a big dent in the body work.
Judge Michael Stokes said it was "premeditated, deliberate murder."
"Why? Because you, obsessed as you were with your former partner and mother of your child, were blinded by jealousy and bent on revenge."
A statement from Mr Pencott's family described him as "honest and hardworking" and called the murder "unprovoked and cowardly".

She was speaking ahead of her party's two-day conference in Glasgow.
Ms Davidson told BBC Radio's Good Morning Scotland programme that she believed the SNP government did not have a mandate for indyref2.
She added that if First Minister Nicola Sturgeon called one she would take a "pretty big hit".
Ms Davidson explained: "I don't think the FM, even by her own measure, has the right to do it [call a second referendum].
"She doesn't have a mandate for it, she doesn't have popular support for it and I think she will take a pretty big hit when you see how many people across Scotland don't want dragged back to a second independence referendum and if she insists on trying to call one I think she will take a pretty big hit."
Prime Minister Theresa May also focused on the issue of independence during a BBC Scotland interview on Thursday.
She told Jackie Bird that the SNP had a "tunnel vision" over wanting a second referendum.
That led Ms Sturgeon to say that Mrs May's Westminster government  had "no mandate" in Scotland.
The PM will address Tory party members later.
Ms Davidson, who will make her keynote speech to the conference on Saturday afternoon, said Ms Sturgeon had failed to show that she had public support for a second independence vote.
She told presenter Gary Robertson: "She [Nicola Sturgeon] also said that she would only have a right to call one if she changed public opinion.
"Now, not only has public opinion not changed, but public opinion over whether to call a referendum has gone, down and down and down."
Ms Davidson was also quizzed about whether Scotland might receive more devolved powers as a result of Brexit negotiations.
She said she had no "ideological objection to absolutely everything coming to Holyrood".
However, the MSP said that the decisions made needed to protect the current market agriculture and fisheries had with the rest of the UK.
A motorist who murdered a love rival when he ploughed into his bicycle at 40mph has been jailed for life.
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Scotland's Conservative leader Ruth Davidson has said there is no popular support for a second Scottish independence referendum.