Dean, 40, joins following a hugely successful spell at National League North side Peterborough Sports, where he enjoyed four promotions in five completed seasons.
He steered them to three titles and 11 trophies in total since becoming manager in 2015, and has been widely acclaimed for his excellent work there, being hailed as one of the best bosses in non-league.
Plummer, 46, was his assistant at Peterborough Sports and will join Dean at Glanford Park. A former England Under-21 international, his playing days saw a lengthy spell at QPR, as well as permanent stints at Barnet and Peterborough United.
During his coaching career, he's managed Peterborough Northern Star, Corby Town and Peterborough Sports, in addition to being part of the England Under-21s set-up.
Nelson, 42, was interim first team manager at the Iron from late November and previously assisted Tony Daws for three months.
He enjoyed a long playing career, including a year's spell at United from 2011, and has previously managed Blyth Spartans, as well as being assistant boss at Hartlepool United.
He enjoyed a long playing career, including a year's spell at United from 2011, and has previously managed Blyth Spartans, as well as being assistant boss at Hartlepool United.