Colindale allotment secretary Lea Adri-Soejoko was attacked by fellow plot-holder Rahim Mohammadi, 42, in February last year.
He throttled her with a lawnmower flex and left her inside a locked shed at the north London site.
Following a re-trial at the Old Bailey, Iranian asylum seeker Mohammadi, from Hackney, was found guilty of her murder.
On the day of his sentencing on Friday, Mrs Adri-Soejoko's grown-up children Tess and Mark described the "torture" of having to sit through two trials.
The siblings stressed that although their mother's killer is an immigrant, they do not believe that is relevant.
Mr Adri-Soejoko said: "Some people make a play about the fact he is an immigrant or refugee, but it's not to do with that.
"Where they come from has nothing to do with it. We are the children of immigrants. This is about the actions of one wicked individual."
Ms Adri-Soejoko added: "Hatred is something you kind of rise to in a situation like this. I'm just glad that the truth has been revealed about him and who he truly is.
"I'm just glad he is not free and will not be able to do this to anybody else."
The pair told how their "happy and vital" mother was "having fun" and living a full life before Mohammadi "stole her from us".
Ms Adri-Soejoko said: "Mum deserved better. She deserved more respect and she deserved longer with her family and was an absolute rock to our family."
She described the long road to justice as "absolutely torturous", adding: "Truth and justice, that's what we wanted and that's what we got.
"What happened to her can never be undone but at least we have a way to move forward."
Mr Adri-Soejoko said listening to the evidence was "incredibly difficult".
He added: "Nobody should ever hear those kinds of things about a loved one.
"Right now it's a huge sense of relief, a huge weight off our shoulders."
Thanking the police and prosecution, his sister said: "Everybody has kept pushing for us and never given up."
A tearful Mr Adri-Soejoko added: "She was our heart - and she still is."
Detective Chief Inspector Noel McHugh, from Scotland Yard, said Lea Adri-Soejoko was a "sprightly" 80-year-old who was loved by all.
By contrast, Mohammadi is a "manipulative, evil, controlling individual", he said.