The 20-year-old forward joins the Glovers from MK Dons for the rest of the campaign.
Zaire-born Tshimanga is a product of the Dons Academy and signed his first professional contract in January 2015 after scoring 36 goals for the Under-18s in the first half of the 2014/15 season.
The youngster made his first-team debut two months previous as substitute in Emirates FA Cup before being loaned out to Aldershot.
Further temporary moves to non-league clubs Chelmsford City, Corby Town, Nuneaton Town and Chesham United followed.
MK Dons took up the decision to extend Tshimanga’s contract for a further season last May before sending him to Iceland for the summer to compete in the Icelandic Premier Division with Throttur Reykjavik.
Tshimanga returned to stadium:mk in July and scored his first senior goal for MK in the EFL Cup against Reading.
He has featured 12 times for the Buckinghamshire outfit this season, including a 71-minute outing in the Dons’ 4-1 defeat to Town in the Checkatrade Trophy.
After capturing the attacker’s servcies, manager Darren Way said: "He played against us so we know he’s a real threat behind a back four and he’s got an eye for goal. Kabongo’s looking to create an opportunity in his career where he can get a run of regular games.
"If he comes here, works hard and trains well then hopefully he can end up like two or three others who’ve come here and gone on to bigger and better things.
"As a player he’s sharp, difficult to mark, secures possession well and is always a threat in behind. They’re the attributes I feel he’s going to bring to the football club and I’m excited to work with him knowing what he demonstrated against us."
Tshimanga’s arrival is subject to ratification from the FA and EFL with the attacker ineligible for tonight’s clash with Plymouth Argyle.