The extension features $60 million guaranteed and will earn Newton $67.6 million in the first three years, according to the source.
The Panthers have called a 6 p.m. ET news conference to officially announce Newton's extension.
Newton, the first pick of the 2011 draft, was in the final year of his rookie contract. Carolina exercised the fifth-year option on that deal last year, meaning Newton was set to make $14,666,666 in 2015 before the extension.
The deal was negotiated between the Panthers and agents Bus Cook, Tony Paige and Chitta Mallik, the source said.
Newton's representatives had been seeking a contract with a high percentage of the money guaranteed and not tied to injuries or other clauses to increase the base value, such as deals the San Francisco 49ers' Colin Kaepernick and Cincinnati Bengals' Andy Dalton signed last year.
Miami Dolphins quarterback Ryan Tannehill, who was picked eighth overall in 2012, recently got a four-year extension worth $77 million in new money with $21.5 million guaranteed. Newton, as the first overall pick in 2011 and a two-time Pro Bowler, was seeking 40-50 percent of his new deal guaranteed.
Newton's overall record is 30-31-1, 1-2 in the playoffs. His 33 rushing touchdowns are the most by any quarterback in his first four seasons, according to the Elias Sports Bureau.
ESPN.com Panthers reporter David Newton contributed to this report.