Expressen says Spurs have agreed a €7.5 million fee with AZ for the young Swede, who was also being watched by Manchester United.
The deal was struck on Tuesday and Elm will move to Spurs at the end of this season. Tottenham wanted Elm in January, but their request was knocked back by AZ.
Elm has agreed terms over a deal to 2015 with Spurs.
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