The 22-year-old joined Nathan Jones' side in the summer after being spotted by chief recruitment officer Mick Harford playing for Truro City.
Vassell has scored twice in 23 appearances and the Hatters have taken up the option in his previous deal.
"Over the five months since he's been here he's done really well to impress us and grasp his chance," said Jones.

The 19-year-old follows Wayne Rooney, Raheem Sterling, Lionel Messi and Sergio Aguero in winning the award for Europe's best player aged under 21.
Rashford and Sanches' club team-mate Kingsley Coman also made the podium.
Portugal international Sanches will receive the award at a ceremony in Monte Carlo on Monday.
The prize, voted for by journalists across Europe, was established by Italian newspaper Tuttosport in 2003, who revealed this year's winner on their front page.
Sanches has played eight games for the German champions this season, having joined in the summer for £27.5m, and has 11 caps for Portugal.
At Euro 2016 - then aged 18 - he became the youngest player to feature in a European Championship-winning side and won the Young Player of the Tournament award.

The Long Island Railroad train went off the tracks as it arrived on Wednesday at Brooklyn's busy Atlantic Terminal.
New York's fire department said 103 people had reportedly suffered "non-life-threatening" injuries.
Passengers on the train said there had been a loud bang followed by a jolt that made some people on the train fall down.
The New York governor, Andrew Cuomo, said the train was travelling at a "fairly slow speed" when it failed to stop on time and struck a buffer at the station.
The impact was hard enough, however, to smash some of the train's windows and crease its doors.
Some of the injured were taken away on stretchers, while others were seen sitting near the train holding ice packs to their heads.
The cause of the accident, which happened at about 08:20 local time (13:20 GMT), has not been determined.
The US Federal Railroad Administration said its investigators were heading to the scene.
Last September, a woman died and more than 100 other people were injured when a train derailed during rush hour as it entered the station in Hoboken, New Jersey. An investigation into that incident is yet to be concluded.
Luton Town striker Isaac Vassell has signed a new contract with the League Two side until the summer of 2018.
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Bayern Munich midfielder Renato Sanches has won the European Golden Boy award, beating Manchester United and England striker Marcus Rashford.
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More than 100 people were injured when a commuter train derailed during rush hour in New York City, officials say.