Both Moore and Willmott spent time under Stringer last season at Bishop’s Stortford and become the Clarets boss’s 13th and 14th new signings ahead of pre-season.
Moore, 22, began his career with Southampton before signing for American side Indy Eleven in March 2014, around the same time that former Manchester United and Brazil midfielder Kleberson signed for the Club.
After a short stint stateside Moore moved back to England to join Forest Green Rovers and had loan spells with Poole Town and Frome Town before signing for Stortford in January 2016.
Willmott, 26, joins after being released by Ebbsfleet United and is a hugely experienced midfielder having made over 100 appearances for Cambridge United across two spells, as well as spending time at clubs such as Luton Town and Newport County.
With chances limited at Stonebridge Road last season Willmott spent time on loan at Eastleigh in the Conference National before joining up with Stringer at Stortford towards the end of last season.
Both will be looking to make an impression on their new boss on Thursday night as the Clarets start their pre-season campaign with a trip to Ryman North side, Heybridge Swifts.