Gauci was among the final players to miss out on Australia's World Cup squad after falling out of favour over the past two years.
The towering South Australian started games in Tony Popovic's first window as coach in 2024, but lost the starting role to Maty Ryan and Paul Izzo, before Patrick Beach's emergence.
That followed a loan stint at Port Vale but it delivered mixed fortunes despite Gauci hitting form late in his time there.
Gauci will now attempt to crack England's second tier with the newly promoted Imps.
"It's a club that's making a step up and that's something that I want to do in my career as well," Gauci told the club's website.
"Having come up against the club last season in League One, I know how competitive they are, how well drilled they are - such a well-oiled machine last season and that was reflected in the league and the results that they had.
"Them making the step up, I also want to progress my career and make the step up to the Championship and to continue to compete to play against the best quality players I can and to play with the best quality players I can."
The 26-year-old won't have it all his own way at Lincoln, given the club announced Gauci would be their No.2 goalkeeper to provide competition to George Wickens.
It means he will have to fight for game time to get back into the Socceroos fold ahead of next year's Asian Cup.
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