The now 39-year-old spent last season with Italian side Cremonese, but his seven goals and two assists in 29 Serie A games weren’t enough to save them from relegation.
Vardy’s one-year contract expired earlier in the summer, and he has since returned to English football, signing until the end of 2026-27.
Speaking to the club’s website, Vardy said: “I’m really happy to now be here at Burnley FC.
"This club has a proper footballing history and passionate fans who deserve a team that represents them and their town.
"I can’t wait to get going on the pitch and help the team move in the right direction.”
Burnley have had a dismal start to the season, sitting rock bottom of the Championship table with two draws and three defeats from their opening five games.