The 24-year-old full-back has signed a two-year deal, having turned down the offer of a new deal with the Pilgrims.
"The last couple of years at Boston I've always wanted to make the step up," said Mills.
"I'll be jumping two steps, but I'm sure I will pick it up quite quickly."
Mills' arrival follows the signing of fellow full-back Danny Andrew from League One side Fleetwood Town.

Exam board Pearson has confirmed plans to develop a new history of art A-level for teaching from next September.
October's decision by the AQA board to drop the subject provoked an outcry from experts who argued "society had never required its insights more".
"It's amazing - just about in the nick of time," said teacher Sarah Phillips.
Ms Phillips, from state sixth form Godalming College, developed the new syllabus with AQA and added: "Now we need to get the message out to Year 11 students as soon as possible."
Subject to approval by Ofqual, Ms Phillips says she expects Pearson to build on her work which has been made available to the Department for Education by AQA.
"It is a global specification. Students won't just study the work of dead white men," she said. "They will have the opportunity to study Islamic architecture and work by men and women of all colours and creeds. The support has been overwhelming," she added.
In October, top experts signed an open letter to AQA condemning the decision not to offer the A-level to new students after this year.
AQA was the last board to offer the subject and the decision represented "a vital loss for students", they argued.
At the time AQA said the change "was not about money or whether history of art deserves a place in the curriculum", but said that it feared the new qualification was so wide-ranging that accurate marking would be impossible.
Pearson, which also announced plans to take on AS and A-levels in statistics, also dropped by AQA, said awarding organisations, government and schools should work together in the interests of students to secure the future of important qualifications.
"The response from the public, from teachers and from young people shows many people have a real passion for these subjects. We're happy to help make sure they remain available," said the company's president, Rod Bristow.
The move was welcomed by leading academics and museum directors as well as by Turner Prize winners Anish Kapoor, Cornelia Parker and Jeremy Deller.
Mr Kapoor said it was "a huge relief" while Mr Deller called it "a good day for art and culture" and added: "Art history is the study of power, politics, identity and humanity, it makes perfect sense to keep the exam."
Ms Parker said she had studied art history "as a working-class girl, receiving free school dinners... It has hugely enriched my life".
The Association of Art Historians hopes the battle to save the A-level will boost the subject's popularity, particularly in the state sector.
"The threat to the A-level has galvanised support for art history, which will, I hope, provide a platform for a concerted effort to ensure that more people get the opportunity to study a subject that will enrich their lives," said Dr Ben Burbridge of Sussex University who was central to the campaign to save the A-level.

An East Midlands Ambulance Service crew found the bin when they tried to leave for hospital in Leicester.
Waste fluid had leaked into the cabin, forcing the vehicle to require a deep clean.
The ambulance was taken out of service and a second ambulance was called. EMAS said the action could have put lives at risk.
The crew was responding to a call in Narborough Road, Leicester, in the early hours of Monday.
Police were notified and the ambulance was returned to service the next day.
Tim Hargraves, an EMAS manager based in Leicestershire, said: "This behaviour is disgusting and can ultimately put lives at risk as this vehicle was taken off the road.
"Our crews work long hours in challenging circumstances and deserve to be treated with respect.
"We will work with Leicestershire Police to support enquiries."
A Facebook post on the EMAS page received more than 1,500 messages of support and was shared more than 4,000 times.

25 November 2016 Last updated at 18:30 GMT
Fazila Aswat and Sandra Major were leaving a car with Mrs Cox ahead of a surgery in Birstall, West Yorkshire, in June when the MP was shot and stabbed.
Promoted Grimsby Town have made their second signing since returning to the Football League by bringing in defender Zak Mills from National League North neighbours Boston United.
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Campaigners for art history A-level say they are "absolutely thrilled" by a late decision to save the subject, which was set to be discontinued.
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A wheelie bin of rubbish was dumped on the front seats of an ambulance as medics treated a patient in the back.
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Jo Cox's assistants, who were with the MP when she was murdered, have spoken about coping with the "surreal" loss of both a colleague and friend.