The 23-year-old was at Peterborough United last season, where he impressed.
He has spent most of his time with the Leicester under-23s in the past four years.
Now he gets a chance for regular first team football, and Wycombe are delighted to have him.
Wycombe boss Gareth Ainsworth said, per the club website: "Josh is someone we tried to bring in during the summer and I'm really pleased to be able to get the deal done. We've been keeping tabs on him for some time and he proved he could make the step up into senior football with a really strong loan spell in League 1 last season.
"He gives us another option in defence and he comes in at an important time as we're working hard to get the team as strong as possible to make sure we can start picking up points and meeting the standard that's required to survive in this division."