The police and military made a chaotic retreat after days of intense fighting.
But the US refused to confirm the capture, saying the situation was "fluid and contested" and it was too early to make "definitive statements".
Ramadi is the capital of Iraq's largest province, Anbar, and is just 70 miles (112km) west of Baghdad.
A statement purportedly from IS said its fighters had "purged the entire city". It said IS had taken the 8th Brigade army base, along with tanks and missile launchers left behind by troops.
A very well-placed source in the Anbar governor's office told the BBC Ramadi was now under the full control of Islamic State, and all government troops had withdrawn. (+ BBC video) » | Sunday, May 17, 2015
