Images have emerged of the group's black banners flying from the top of every lamp post in one main street.
Locals have also reportedly been forced to participate by putting posters and decorations on important buildings.
The fall of Mosul came as a shock to many and prompted the jihadist group to launch an offensive that saw it seize swathes of Iraq.
More on this story:
Inside Mosul: Life under IS control
On the front line in battle for Mosul
Footage reveals IS regime in Mosul
What has happened since the fall of Mosul?
Despite facing 10 months of air strikes by a US-led international coalition and attacks on the ground by Iraqi government forces, IS has maintained its grip on the territory and been free to impose its extreme interpretation of Islamic law.
On Tuesday, the Iraqi satellite channel al-Sumariyah TV cited a local official in Mosul as saying that IS was expected to hold a "victory" celebration at the former five-star Nineveh Hotel, which has been taken over by the group.
There were unconfirmed reports that IS leader Abu Bakr al-Baghdadi would make an appearance or issue a recorded message to mark the occasion, al-Sumariyah added.
Last July, Baghdadi delivered a sermon at Mosul's Great Mosque in which he urged Muslims to emigrate to IS territory in order to carry out a war for the faith against unbelievers. It came days after IS formally declared the establishment of a "caliphate" headed by Baghdadi.
Sources in Mosul told the BBC that IS militants were also undergoing training in the streets on Tuesday in preparation for a government offensive.
Mosul had been expected to become the focus of a lengthy campaign after the government recaptured the northern city of Tikrit in early April.
But US officials said the fall of the western city of Ramadi to IS last month meant it was likely to be delayed, possibly until 2016, the New York Times reported.
The Mosul operation depends on the success of US efforts to retrain the Iraqi army, whose soldiers fled Ramadi despite vastly outnumbering the IS militants attacking.
Islamic State (IS) militants in Mosul have been marking the first anniversary of their capture of Iraq's second city.