The findings may lead to new ways to help people remember things better, researchers said.
Earlier studies have shown that the number of spindles that occur during the night could predict a person's memory the next day.
The study, published in the journal Current Biology, has also shown that the content of reactivated memories can be decoded for brain activation patterns at the time that spindles occur.
The team devised an experiment in which people learned to associate particular words with particular objects and scenes.
Some study participants then took a 90-minute nap after their study session, whereas others stayed awake.
The results showed them that sleep spindles occurred when memories were reactivated by presenting the associated words.
Researchers were able to differentiate the brain signals associated with reactivated objects and scenes. This demonstrates that spindles produce a specific code for the content of reactivated memories - a process that may underpin our ability to remember more after sleep.
"While it has been shown previously that targeted memory reactivation can boost memory consolidation during sleep, we have now showed that sleep spindles might represent the key underlying mechanism," said Bernhard Staresina from University of Birmingham.
"Thus, direct induction of sleep spindles - for example, by stimulating the brain with electrodes - perhaps combined with targeted memory reactivation, may enable us to further improve memory performance while we sleep," said Staresina.
"We are quite certain that memories are reactivated in the brain during sleep, but we do not know the neural processes that underpin this phenomenon," said Scott Cairney from the University of York.
"Sleep spindles have been linked to the benefits of sleep for memory in previous research, so we wanted to investigate whether these brain waves mediate reactivation," said Cairney.
The findings may help to explain how that process may go wrong in people with learning difficulties, according to the researchers.
It might also lead to the development of effective interventions designed to boost memory for important information.