Elliott will now remain in charge until the summer of 2022 following an historic Emirates FA Cup run, culminating in a second round replay defeat to Rochdale, and having the Pilgrims well-placed for a tilt at promotion in the New Year.
He has won 47 of his opening 101 matches in the United hotseat, having assumed control in November 2017.
Reflecting on the new contract for Elliott, Mr Newton commented: "I am delighted that Craig has accepted an offer to extend his current contract.
"He has worked really hard since he joined Boston United and has now assembled a squad that is capable of challenging at the top of the division and, of course, we have just come off a great FA Cup run, although contract discussions took place ahead of that.
"His aspirations match ours and it's a pleasure to work with him as we all try and deliver success on and off the pitch for the fans at this very exciting time for the club.
"I wish Craig the very best of luck."
Elliott added: "I am delighted to accept a contract extension at Boston United.
"A lot of hard work has taken place since taking over a team that was second bottom. I now feel we are seeing the club going in the right direction on and off the pitch.
"I have a great working relationship with David and Neil and both share the same vision as myself to continue to improve and achieve success at this great club.
"The future is looking very exciting and I want to be part of this journey and will be working as hard as I can to achieve this.
"The heartbeat of this club is the fans and my motivation will be to give them a team week in, week out that they can be proud of."