The 29-year-old has linked up with the Pilgrims from National League North rivals Alfreton Town, having spent the last two seasons at the Impact Arena.
Shiels also has considerable Step 2 experience to his name with Harrogate Town, whom he helped reach the National League North play-offs in 2015-2016.
United manager Craig Elliott was understandably delighted to clinch the signing of Shiels and told bufc.co.uk: "He is the leader we have been after for a while.
"Luke is strong and aggressive and attacks the ball in both boxes.
"He has vast experience at this level and I am very much looking forward to working with him."