The trio are being offloaded by the Storm as they try and comply with salary cap regulations in Australia following a large, well-publicised breach this season which has resulted them in being stripped of all their points and their NRL titles from recent seasons.
The arrival of second-rower Hoffman, 26, is likely to spell the end to Phil Bailey‘s Wigan career, with the Australian international signing a one-year deal, with the option for a second.
Half-back Finch, 28, had been linked with Hull KR but has signed a two-year deal with the Warriors while Kiwi test prop Lima, 28, has signed a three-year deal, with compatriot Iafeta Palea’aesina now likely to be on his way out of the club.
Boss Michael Maguire, who was assistant coach at the Storm up until this season, said: “Having worked with all three during my time at Melbourne, I am thrilled that they will be joining us from next season.
“All three are champion players with experience at the very highest level.
“They have a great work ethic and are top-quality additions who will complement our existing playing squad.”