Armstrong made his Premier League debut last August and has since featured six times for Everton’s first team.
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The England Under-18 international secured his temporary move to Pride Park on the same day he signed a new long-term contract with Everton.
"Getting the chance to play for the first-team this season has been great and I just want to push on and reach more," Armstrong told the Everton website.
"I now have an opportunity at a really good club like Derby to learn and hopefully do well for them and I'm looking forward to it."