The 30-year-old, who has moved to Turf Moor for an undisclosed fee, made 13 appearances for Birmingham during the 2017-18 campaign.
Legzdins started his professional career with the Blues, but left to join Crewe Alexandra in 2008, and represented Burton Albion, Derby County and Leyton Orient before returning to Birmingham in 2015.
"Interest from someone like Burnley is something you can't ignore, no matter what the situation was at Birmingham, and after speaking to the people here I think it will be a really good fit for myself," Legzdins told Burnley's official website.
"I'm looking forward to working hard to see what happens. I'm looking forward to working with the goalkeepers that are already here."
Burnley will open their new Premier League season with a trip to champions Chelsea on Saturday afternoon.