News of Hunter's pending agreement with the team was first reported by the Philadelphia Inquirer. Sources told The Athletic that Hunter's deal is for two years and worth around $18 million.
The 31-year-old Hunter spent last season with the Tampa Bay Rays, striking out 64 in 58⅔ innings of work, all in relief.
Hunter pitched for a 2.61 ERA last season, the lowest ERA in Hunter's 10 seasons in the majors.
ESPN incorrectly reported earlier that the Phillies were nearing a deal with free-agent reliever Addison Reed.