The 24-year-old defender is arriving as a replacement for Ben Chilwell.
And The Sun says Leicester will pay roughly £21.5 million for the player.
Castagne has passed a medical in Germany while on international duty.
Now he will join on a five year deal, and should slot right into Brendan Rodgers starting lineup for the coming season.
He played 33 games for Atalanta last season, scoring three goals in the process.