The 6ft 5 inch striker has been a target of Boro boss Darren Kelly for some time.
Simpson also played for Hartlepool United and signs subject to international clearance.
The striker, 20, reuinted with Kelly who had him during a very successful loan spell with Hyde United, which included a goal at the Flamingo Land Stadium.
Simpson had previously been linked with Premier League giants West Ham, before making a move to play for Championship club Preston.
He has most recently been playing his trade in Ireland with Cork City.
Boss Kelly said:
"I've kept in touch with Connor over the past couple of years and during the summer I was contacted by a few higher league clubs about his availability. He has been a huge target for me for quite some time and I'm absolutely delighted to bring him in. It would have been very easy for Connor to go higher on much bigger money, but I've had a good chat with him about the club and he is very excited about playing for us. I know what he is about, what he will bring to our team. He has a lot of strengths and I am looking forward to utilising them. He is a big, strong lad, who can hold the ball up, but he is also very quick. I can't wait to see him up front with the other excellent attacking options we have at the club."
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