Hudson, 20, joins from league rivals Ashton United, having started out at Leeds United and moving to Darlington upon his release. He has also represented England at Under-16 level.
Boro have also signed Harker on a short-term basis.
The 22-year-old stopper, who has previously been with Newcastle United and Sunderland, will be involved in Saturday's game in the absence of Ryan Whitley and Michael Ingham.
Both players go into tomorrow's squad having completed the signings before the lunchtime deadline.
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Tomorrow's FA Cup tie kicks off at 3pm at the Flamingo Land Stadium and is all pay on the gate.