Sky Sports says the Swedish striker successfully completed the mandatory medical tests this Saturday morning.
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Gyökeres is now heading to Singapore to join his new teammates.
It's the end of a protracted transfer saga. At one point, the deal with Sporting Lisbon threatened to fall apart, but a deal was finally agreed.
The Gunners are reportedly transferring €63.5m to Portugal for the 26-time capped international. A further €10m could follow in bonuses.