If the deal is finalized, the veteran quarterback would receive in excess of $120 million over six years, according to a person close to the negotiations who spoke on condition of anonymity because the contract has not yet been signed.
Flacco played out his rookie contract last season for $6.76 million and led Baltimore to the NFL championship.
Ravens general manager Ozzie Newsome said the sides have settled on the parameters of the deal, but still have some language and details to work out.
Fox Sports first reported the new deal.
Reaching agreement with Flacco before Monday's 4 p.m. franchise deadline means the Ravens are assured of retaining their starting quarterback and don't have to take a salary cap hit of approximately $19.5 million.
On Feb. 7, Newsome said, "If we are able to get a deal done, it will allow us to participate more in the (free agent) market, if we so choose."
The 28-year-old Flacco is the only quarterback to win a postseason game in each of his first five pro seasons. He had a spectacular playoffs and Super Bowl this year, throwing for 11 touchdowns with no interceptions.
He also holds the record for playoff road wins with six.
"We've never lost a great, great franchise player from the beginning," Bisciotti said. "I'm just very comfortable that it will get done."
On Friday, it did.
Flacco was a first-round draft pick in 2008 out of Delaware and one of the most consistent postseason winners in NFL history.
Flacco said after the Super Bowl victory over San Francisco that he expected to be back in Baltimore. He made sure of that Friday, coincidentally hours after the franchise tag figures for 2013 became known.
Had Flacco been franchised, he would have earned at least $14.896 million this season.