Muhammad Javid, 20, of Evington Road, Leicester, drove into Victoria Gayle, 25, from Canada, in Upperton Road, just before midnight on 6 June.
Ms Gayle, who was visiting the UK and had been cycling at Bradgate Park, later died in hospital.
Her mother Carol said the family was "shattered" by her "untimely death".
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Mrs Gayle said her daughter had just graduated from the University of Toronto and hoped to study law in the UK.
"Nothing could have prepared us for the shock of seeing my daughter laying in the hospital bed lifeless," she said.
Javid's speed had reached 67mph on a 30mph road shortly before the accident and he was still travelling between 32 and 40mph when he hit Ms Gayle, Leicester Crown Court heard.
He also left the scene of the accident but returned shortly afterwards.
Jeremy Janes, prosecuting, said Javid's car had been heard revving loudly shortly before the accident.
He said: "One witness walking up the road described the Yaris as being driven 'like a boy racer'. I can't improve upon that."
Judge Robert Brown said: "You drove your car too fast in a built-up area where pedestrians are always likely to be present.
"The accident reconstruction expert has shown that if you had been driving within the speed limit, your braking would have made you stop before impact."
Javid pleaded guilty to causing death by dangerous driving and failing to stop at the scene.
He was given a 40-month custodial sentence and will serve 20 months at a young offenders institution before being released on licence. He was also disqualified from driving for 56 months.
A man who killed a cyclist while driving "like a boy racer" has been detained for causing death by dangerous driving.