Retaking the town - at Nigeria's border with Chad, Niger, and Cameroon - is particularly important as Baga was the headquarters of a multinational force of troops from all four countries.
Boko Haram had claimed a January 3 attack that killed scores, possibly hundreds, and left its fighters in control.
"We have secured Baga. We are now in full control. There are only mopping up exercises left to do," Major-General Chris Olukolade, an Nigerian defence spokesperson, told Reuters news agency by telephone.
In a statement minutes earlier Olukolade had said that "a large number of terrorists had drowned in Lake Chad" as troops advanced on Baga.
Al Jazeera could not independently confirm the government's report.
The fighters appear to be on the run in many parts of Nigeria and regions near its borders, after being subjected to a major offensive on all sides, reported Reuters, adding that although they have come close to being defeated in the past, they have bounced back deadlier than ever.
"Not even the strategy of mining over 1,500 spots with landmines on the routes leading to the town could save the terrorists from the aggressive move of advancing troops," Olukolade had said in a statement earlier in the day.
Al Jazeera's Yvonne Ndege, reporting from the Nigerian capital Abuja, said the military has confirmed the report.
"This is a significant moment, a symbolic victory," she said. "But it is very difficult to know precisely how successful the operation was."
Successes in pushing back Boko Haram are welcome news for Nigeria's President Goodluck Jonathan as he faces an election on March 28 that was delayed by six weeks on the grounds that more time was needed to fight the campaign.