The Scottish defender, 22, made one senior appearance for the Magpies, starting at the heart of defence in a 3-1 Emirates FA Cup win over Birmingham City in January 2017.
He had joined United from Celtic in July 2016 but was released this summer.
Findlay spent a successful loan spell with Kilmarnock last season and has now agreed a three-year deal at Rugby Park, subject to international clearance.
Meanwhile, teenage midfielder Mace Goodridge has signed for Burnley after being freed by the Magpies.