The deal has a no-trade clause but no opt-out clause, the newspaper reported, citing several sources.
"The sky's the limit for him," Phillies manager Gabe Kapler told the Inquirer. "There's really no ceiling."
The contract of Harper, 26, the 2015 National League Most Valuable Player, topped the 13-year, $325 million extension Giancarlo Stanton received from the Miami Marlins in 2014.
Harper will receive a $20 million signing bonus and a $10 million salary for the 2019 season, ESPN reported. Harper will be paid $26 million annually from 2020 to 2028 and $22 million per season from 2029 to 2031, the website reported.
Harper has spent his entire seven-year career with the Washington Nationals. He has a .279 career batting average, with 184 home runs and 521 RBI.
Manny Machado agreed to a 10-year, $300 million deal with the San Diego Padres on Feb. 19.
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