Johnson has had only a bit-part to play at Glanford Park this season after joining on a free transfer in the summer.
He has been unable to dislodge the front pairing of Billy Sharp and Andy Keogh, and agreed last week to move to the Lambs in the summer.
Manager Brian Laws told the SUFC website: "Tommy wants to play regular first team football, we cannot guarantee him that so have agreed to let him go on loan."