The Queenslander has been a prolific run-scorer in his home country, with 927 first-class runs in the 2011/12 domestic season and just short of 1,000 in the most recent summer.
He top-scored with 43 as the Brisbane Heat beat the Perth Scorchers in the Big Bash final, averaging 31 across the tournament, and made 141 against the England Lions last month.
"I'm very excited to get the opportunity to join Leicestershire for the 2013 season. In my discussions with the staff of LCCC, I feel this is a fantastic opportunity personally for myself to continue to develop my cricket and to perform at the highest level," the 23-year-old said.
Burns will be an alternate overseas player to Ramnaresh Sarwan, who is expected to be on West Indies duty for large parts of the year.
Burns will arrive on May 15 and leave on August 30, taking in the full Twenty20 tournament in the process.
Leicestershire have also confirmed the signing of former Zimbabwe international bowler Anthony Ireland on a one-year contract.