That led the Argentine club to take the case to the Court of Arbitration for Sport (CAS), who presided over the final ruling.
Velez claim City acted unethically by approaching Garre when he was just 15, before signing him days after his 16th birthday.
Cas has now upheld that verdict after a hearing took place a year ago.
Velez complained to Federation Internationale de Football Association in 2016 that City broke rules preventing trafficking of minors by signing Garre after he turned 16.
A formal announcement is expected from the CAS later this week, and Velez could yet make a technical appeal against its decision.
City argued that Garre held an Italian passport and was entitled to move after his 16th birthday.
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As such, City facing the prospect of being banned from registering players in each of the next two transfer windows - a fate suffered previously by Atletico Madrid - if the CAS side with Velez.
Having already seen their case upheld by FIFA, Manchester City were always confident that the CAS would rule similarly, and have received a positive result.
Spanish giants Barcelona, Real Madrid and Atletico Madrid have been banned for breaching rules governing the signing of worldwide players under the age of 18 in recent years.
"We're angry because City came after our player, we said no and they took him anyway", declared Velez club secretary Bernardo Bertelloni a year ago.
Federation Internationale de Football Association bans the transfer of under-18s to different countries unless they meet strict criteria.
The FC crew delve into Man City's evolution during Pep Guardiola's second season in charge and debate whether winning the Premier League put his critics to bed. It brought in the rules to help protect children from exploitation and trafficking.
Velez, however, claimed that Federation Internationale de Football Association rules only allow players under 18 to move between clubs in Europe and does not include South America. Even then, the buying club must meet more criteria relating to education, training, living conditions and support.