As part of Operation Inherent Resolve the US, France and the UK carried out almost daily air strikes in the fight against IS in Iraq and Syria.
Amnesty International and monitoring group Airwars said their joint investigation looked at 200 strike locations in the city, interviewing more than 400 witnesses and survivors and identifying 1,000 victims.
Donatella Rovera, from Amnesty, said: "Many of the air bombardments were inaccurate and tens of thousands of artillery strikes were indiscriminate, so it is no surprise they killed and injured many hundreds of civilians.
The report said many of the cases "are likely to amount to violations of international humanitarian law".
A spokesman for the Ministry of Defence (MOD) said: "Sadly, no military action can be wholly without risk - we do everything possible to mitigate those risks, but cannot eliminate them entirely.
"Global coalition air strikes have successfully contributed to the liberation of all the territory once held by Daesh, who imposed unspeakable suffering on millions of people."
The MOD spokesman added: "After every UK air strike we conduct a thorough battle damage assessment, which uses all available information to examine the outcome of the strike, and also looks very carefully at whether there is any evidence of civilian casualties or damage to civilian infrastructure."
Previously Operation Inherent Resolve has said that at least 1,257 civilians have been unintentionally killed by coalition strikes in both Iraq and Syria since the start of the campaign in August 2014.
By February this year, the coalition had conducted 34,038 strikes.