Archer, 19, has impressed since arriving on loan from Spurs in the final week of September.
The Scotland Under 21 international has appeared 12 times in goal for the Blues, keeping three clean sheets in the process.
Manager Gareth Ainsworth told Wycombe's official website: "We're really pleased with the way Jordan's settled into the squad and his level of performance.
"He's made his professional debut and is gaining valuable experience of playing first-team football.
"I'd like to thank Tottenham for allowing us to keep Jordan for the rest of the season. We are very grateful."
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