Well known for being a qualified doctor, Kenny will continue to practice medicine whilst playing for Livi.
Deuchar was a prolific scorer for East Fife and then Gretna, playing a major part in their meteoric rise to the Scottish Premier League.
The striker has also had spells with Northampton, Major League Soccer club Real Salt Lake, Hamilton Accies and St Johnstone.
Deuchar joined Falkirk for a second stint last summer but has been confined to the substitute's bench for most of the campaign.
Source: BBC Sport