Jackson, 23, previously worked with Holy Blues boss Curtis Woodhouse at Bridlington Town and becomes the sixth player committed for the 2020/21 season.
Woodhouse said: “I’m delighted to welcome Tom to Gainsborough Trinity, a goalkeeper I had at Bridlington Town and quickly realised he would soon be playing at a lot higher level.
“Tom is a goalkeeper I believe can go all the way in the game and we are delighted to have secured his signature for next season as lots of teams wanted him, so it’s a real coup for us.
“Tom excelled again at Frickley and all the scouting reports we got back said the same thing about Tom being the best goalkeeper in the league. I’m delighted he’s chosen Gainsborough Trinity and I look forward to working with him again and developing his game.”
Gainsborough had earlier this week confirmed their released and retained list, which confirmed that Jack Walters, Gregg Smith, Alex Wiles, Declan Bacon and James Williamson are on deals for next season.
The new number one will link up with goalkeeper coaches Charlie Cresswell and Leigh Herrick.
Jackson said: "I just can't wait to get going as soon as it is safe to do so. I know we've only had six or seven weeks of lockdown, but I just want to get cracking! I have played under Curtis at Brid, he actually took me there and gave me my first chance. I had a good season there, before stepping up to Frickley and had another good season, so to then have the interest from Curtis was brilliant.
"As soon as we had spoken about Trinity's aims, the new training facilities - it was a no brainer. I definitely see this as the next step in my career, being part of the success that Gainsborough Trinity are going to have."