The FA said in a statement on Monday that authorised agent Alan Middleton and unlicensed agent Philip Ercolano were both involved in the deal.
The transfer fee was undisclosed by the clubs but media reports at the time put it at 15 million pounds ($23.06 million) for defender Chambers who now has three England caps.
"Alan Middleton has also been warned as to his future conduct and sanctioned for breaching the FA's football agent regulations in relation to the same matter," the FA added.
Middleton has been fined 30,000 pounds and given a suspended ban of three months.
"We acted in good faith throughout in this transfer and had no reason to believe that the player's representative (Ercolano)was not authorised to be involved in the transfer negotiations," said an Arsenal statement.
"The FA fully recognised that there was no intention to mislead on Arsenal's part. We have improved our procedures to prevent this happening again."
Arsenal travel to Championship club Sheffield Wednesday for a Capital One Cup fourth-round tie on Tuesday.
(Reporting by Steve Tongue; Editing by Tony Jimenez)
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