The self-confessed Hoops fan also acknowledged some supporters of the eight-in-a-row champions will never forgive him for leaving the Parkhead outfit.
Tierney, 22, had been linked with the London side for almost a month before their offer was accepted.
The defender has now played twice for the Gunners – wins against Nottingham Forest in the Carabao League Cup and Standard Liege in the Europa League – and is standing by to make his Premier League debut against Bournemouth tomorrow.
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Source: KT REVEALS CELTIC SORROW