Midfielder Marshall, 32, brings plenty of experience to the Premier Division side. His previous clubs include Manchester City, Aberdeen and Stockport.
The club also announced the signings of Taylor Jones, Sully Sassad and Omar Ibrahim.
Jones, 19, is a defender who joins Radcliffe from Oldham Athletic.
Goalkeeper Sussad makes the switch from division rivals Matlock Town, while Ibrahim, 21, joins from Norrvalla FF in Finland.