Earlier today Iraq announced victory against IS in the northern city, the country's second largest, from where the group declared a self-styled caliphate three years ago.
Battles have raged for months, leaving thousands dead and wounded, while nearly a million people have fled.
"I congratulate Prime Minister (Haider) Abadi, and the Iraqi forces who have been fighting on the ground with great bravery and care against a brutal opponent," Fallon said in a statement.
As part of Britain's involvement in the US-led coalition against the jihadist group, Fallon said British forces had struck 750 targets in the battle for Mosul.
But "there is still more to do" around the city and in the broader region, Fallon said.
"This barbaric group remains dug in west of the Euphrates and clearing operations in and around Mosul will be needed because of the threat from improvised explosive devices," he added.
IS holds territory elsewhere in Iraq and in Syria, where the US-backed Syrian Democratic Forces (SDF) are battling to oust the jihadist group from its stronghold Raqa.
The coalition against IS launched military operations in the two countries in mid-2014, while Iraqi forces launched their campaign to recapture Mosul in October.
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