CSN Sports' Jim Salisbury was the first to report a deal was close to getting done between the two clubs.
Hellickson, 27, is expected to make more than $6 million in his final season of arbitration before free agency. The Phillies are rebuilding and will have Hellickson in their rotation for at least the 2016 campaign.
Philadelphia's rotation, which does not have a notable amount of depth beyond Aaron Nola and Jerad Eickhoff, will likely benefit from the addition of Hellickson.
After being named American League Rookie of The Year with the Rays in 2011 and having success in 2012, Hellickson has had difficulty being consistent and has become a back end of the rotation starter. Over 146.0 innings with the Diamondbacks last season, Hellickson pitched to a 4.62 ERA and 4.44 FIP.
Minor league pitcher Sam McWilliams is heading to the Diamondbacks in the deal, according to MLB.com's Todd Zolecki.
McWilliams, 20, tossed 33.0 innings and pitched to a 3.27 ERA for Philadelphia's Gulf Coast affiliate in 2015.