The 32-year-old former Oxford and AFC Wimbledon striker scored 11 goals in 83 games for Eastleigh over two seasons, but failed to find the net in 2015-16.
Midson is the seventh summer signing by last term's play-off semi-finalists.
"I think he got a bit frustrated last season but he's raring to go and will do really well for us," Iron boss Jamie Day told the club website.
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Braintree Town have signed Jack Midson on a one-year deal after his release by National League rivals Eastleigh.