City had been close to completing the deal in January for £200,000, but it has taken until now for Kilmarnock to confirm an agreement had been reached.
Smith, 16, will join the Elite Development Squad with immediate effect.
Kilmarnock said in a statement: "Liam has been a supremely talented member of our youth teams and has helped our U18s reach next month's Scottish FA Youth Cup final as well as playing for Scotland U17s earlier this term.
"The deal, the terms of which remain undisclosed, takes account of Liam's prodigious talent and future potential."
Speaking about the transfer, Kilmarnock Head of Football Operations said: “While we had hoped to see Liam continue his development at Rugby Park and are disappointed to be losing him, we fully understand and appreciate the opportunities moving to Manchester City will provide Liam both on and off the pitch. We wish him every success at Manchester City."
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