The 26-year-old will be available for all three competitions, but will not be able to play against his parent club.
In 12 first-class games for Somerset and Surrey, Burke has scored 274 runs, with a highest score of 79, and taken 23 wickets at 28.13.
"It is important for us to have depth and James is highly talented," head coach Pierre de Bruyn said.
"James will add strength to our batting and bowling, and he is also a dynamic fielder."
Leicestershire finished seventh in County Championship Division Two last season, and they were knocked out in the group stages of the One-Day Cup and T20 Blast.
Leicestershire have signed Surrey all-rounder James Burke in a loan deal for the entire 2017 county season.