After signing a 12-month deal with the First Division outfit, Deuchar said he was relishing a new challenge.
"I'm absolutely thrilled to be a Falkirk player again," he told the club website. "I am desperate to help take this club back to the Premier League."
Deuchar also enjoyed spells at Hamilton Academical, East Fife, Gretna, Northampton Town and Real Salt Lake.
The striker said remaining at McDiarmid Park was an option but stressed that he was attracted to the challenge of helping Falkirk back into Scotland's top flight.
Kenny has a proven track record of scoring goals
Falkirk manager Steven Pressley
"I could have gone to a number of First Division clubs or stayed at St Johnstone, but this is where I want to be," Deuchar said.
"I read a quote last season from Ryan Flynn saying that he felt like coming back here was like returning home and that's exactly how I feel now."
Falkirk manager Steven Pressley said Deuchar would bolster his attacking options for their tilt at the First Division title.
"Kenny has a proven track record of scoring goals and I believe he is a player that has continued to improve with both age and experience," he said.
"At 29, we are arguably getting him at his prime."
Deuchar, former Rochdale winger Kallum Higginbotham, Mark Millar and Jason Marr, who both arrived from Celtic, met their new team-mates at training on Thursday.
Source: BBC Sport
Source: BBC Sport