The Major League Baseball website on Wednesday cited a source saying that Burnett would receive $16 million, a figure that is projected to push the Phillies to a franchise-record payroll of about $174 million.
The National League club has not confirmed the signing.
Burnett, 37, went 10-11 for the Pittsburgh Pirates with a 3.30 earned run average last season, leading the National League with 9.8 strikeouts per nine innings.
The right-hander is 147-132 in a long career with four MLB teams.
Burnett's apparent signing comes in the wake of news that left-handed starting pitcher Cole Hamels, who is rehabbing biceps tendinitis, will not be ready to pitch on opening day.
Hamels was 8-14 with a 3.60 ERA last season, when the injury-hit Phillies posted a 73-89 record.
(Reporting By Andrew Both in Cary, North Carolina; Editing by Larry Fine)