The sponges melt away over time, leaving only the repaired tooth.
"The simplicity of our approach makes it ideal as a clinical dental product for the natural treatment of large cavities, by providing both pulp protection and restoring dentine," said Prof Paul Sharpe, the study's lead author, of the Dental Institute, at King's College London.
"Using a drug that has already been tested in clinical trials for Alzheimer's disease provides a real opportunity to get this dental treatment quickly into clinics."
Currently, dentists use man-made fillings to treat cavities but these fail to disintegrate, meaning the mineral level of the tooth is never completely restored.
The new technique could reduce the need for fillings, which are prone to infection.
The study was published in the journal Scientific Reports.