Both Premier League giants were in talks with Hearts over a deal for the highly regarded 18-year-old, but Tottenham have come out on top.
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According to Fabrizio Romano, Arsenal were only offering Wilson a trial, something that Hearts were reluctant to sanction.
Wilson is now set to join Spurs on an initial loan with an option to buy in the summer, although it is unknown how much that potential fee would be.
The striker broke into the Hearts first team this season but has only managed to start one of his six Scottish Premiership games.