Abadi "announces the liberation of Tikrit and congratulates Iraqi security forces and popular volunteers on the historic milestone," his official Twitter account said, referring to allied paramilitaries who have played a major role in the fighting.
And Abadi's spokesman Rafid Jaboori told AFP that: "Iraqi forces reached the centre of Tikrit, raised the Iraqi flag and are now clearing the city."
But it was not immediately clear if resistance in the city by the ISIS group had ended entirely, and the massive challenge of defusing explosives planted in roads and houses remains ahead.
Iraqi soldiers and police and Popular Mobilisation units -- paramilitary forces dominated by Shiite militias -- began the battle to retake Tikrit on March 2.
They were able to recapture towns near Tikrit and then surrounded it, but faced difficulties pushing into the city and the operation stalled.
Iran had been the main foreign backer of the operation and some militiamen accused Washington of attempting to hijack their victory, AFP reports.
ISIS spearheaded a major militant offensive that overran much of Iraq's Sunni Arab heartland last June, and some parts of Nineveh and Anbar provinces are still under their control.