Gooda, 22, came through the ranks at Barnsley before spells with Harrogate Town and Frickley.
Tigers assistant John McCombe said: "We are delighted to have Bailey on board for next season and he fits perfectly into the profile of player we are trying to bring into the football club.
"He did very well at Scarborough last season and we were very surprised to see him get released at the end of the season.
"He is a good centre half who is comfortable on the ball and has a wealth of experience for his age. He has shown a great desire to join the football club and has turned down better financial offers as he believes this is the best place for him to progress.”
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