The 20-year old, who was with the Hammers since the age of eight, has joined the Sky Blues for the rest of the 2014/15 League One season after the mutual termination of his contract at Upton Park.
City manager Steven Pressley said: "I'm delighted to complete the signing of Blair as we've been looking to add to our attacking options throughout the window.
"Blair is a player who has demonstrated a great deal of potential during his career and we believe we can help him realise that potential during his time at the club.
"He gives us a real threat on the wings for the rest of the season and I hope he can use his time at the club to earn a long-term deal."
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