Burnett and the Phillies have to work through some additional details before the deal will be announced, the source said. One of those details, according to the source, is the addition of a possible player option or mutual option to the agreement.
The 37-year-old Burnett spent the past two seasons with the Pittsburgh Pirates. The right-hander went 10-11 with a 3.30 ERA with team highs of 191 innings pitched and 209 strikeouts last season, helping Pittsburgh reach the postseason.
In October, Burnett told a Pittsburgh radio station that he would return to the Pirates as a free agent this year or retire.
Burnett spent much of the winter mulling over his decision before deciding in late January that he wanted to pitch in 2014.
The Phillies, Pirates and Baltimore Orioles expressed interest before Burnett agreed to terms with Philadelphia.