The 22-year-old, who is capable of playing at centre-half or in the centre of midfield, sealed his move to The Jakemans Stadium late on transfer deadline day on Thursday afternoon.
Broadhead began his senior career with Chesterfield, spending two seasons as a professional at the Proact Stadium while also enjoying loan spells in non-league with the likes of Buxton, Worksop Town, Matlock Town and Frickley Athletic.
He is eligible to make his United debut against Salford City on Saturday and his signing concludes the Pilgrims’ transfer business for 2016-2017.