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."