The United States-born 21-year-old was with Dumbarton last season.
"I am excited about the year ahead as I have forced my way into the Republic of Ireland U21s starting XI," he said.
"I was number two for a few years. Hopefully I can keep my spot and get some caps under my belt, which will be a great experience."
Rogers has yet to break into the Dons first team and Danny Ward has arrived on loan from Liverpool to challenge Jamie Langfield and Scott Brown for a starting place at Pittodrie.
So the goalkeeper, who has played three times for Republic of Ireland Under-21s and played 36 times for Dumbarton, was happy to leave on a third loan spell, having also played for Airdrieonians.
"I feel, at this stage of my career, it is important to try and play on a regular basis and going to Falkirk will hopefully give me that opportunity," he told Aberdeen's website.
"It is up to me to go to Falkirk and do well and then to come back next season to Aberdeen and challenge for that number one jersey.
"I feel my career is going in the right direction and I just need to keep working hard.
"Falkirk are a big club who have big expectations and had a good season last year and will be looking to kick on this year."
Falkirk manager Peter Houston told his club website that he regards Rogers as "a fantastic prospect".
Aberdeen goalkeeper Danny Rogers hopes returning to the Scottish Championship on a season-long loan with Falkirk will boost his international chances.