The 22-year-old featured regularly for the club’s development side but was unable to break into the Easter Road first team, instead spending time on loan with Gala Fairydean Rovers across two spells before impressing last season on loan at Hibs strategic partner club Stenhousemuir.
Martin kept six clean sheets for the Warriors and won plaudits for his performance in a Scottish Cup clash with Kilmarnock, despite Stenny falling to a 4-0 defeat.
Falkirk manager Paul Sheerin said: “We’re really happy to welcome Paddy and Luke to the club and both Tony and I have been impressed with their abilities during pre-season.
"We knew coming into the club that we needed strong competition in the goalkeeping department and alongside Robbie Mutch we now have that.
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"We expect one of our new goalkeepers to head out on loan to get valuable experience but with the ability to be recalled at any time.”