Fahy, 22, who hit 18 goals for the Swans last season as top scorer, had been chased by several other clubs including Yate Town and Swindon Supermarine.
Slimbridge boss Leon Sterling is not planning to sign a replacement and hopes that the rest of the team will contribute extra goals.
He told www.gazetteseries.co.uk: “Paul is a good lad and had a good season. As a striker who scored that number of goals, he was always going to attract interest.
“I was aware of it halfway through the season when Swindon Supermarine came looking but we are not a one-man team. We wish him all the best and now it is up to the lads to get goals."
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