The 17-year old Czech Republic stopper has attracted plenty of interest from big clubs around the world but it is believed that the Blues have paid £5million to secure the youngster.
The news has not been made public with Sigma confirming a deal but refraining from naming the other club involved.
"A spell at a top European club for Tomas Kala was successfully arranged today," read a statement on the club's official website.
Kalas' agent Pavel Zika told sport.cz: "We cannot confirm the club's name yet.
"Negotiations were very difficult and I am glad they are behind us now, especially for the good of the player."