The 20-year-old forward hasn't played a first team game for City in over four months, and so will join the Seadogs for a month to get some competitive football under his belt.
Boro - 7th in the Conference and 4 points off a play-off spot - had tried to sign him previously but were denied due to a transfer embargo placed on them because of their administration. However, after appealing the transfer has been sanctioned.
Meanwhile, Clayton Donaldson - a regular strike partner for Bradshaw in the Juniors and Reserves at City - signed a two year professional contract prior to Saturday's game against Lincoln, in which he came off the bench to make his league debut.