The Premier League teams will face each other at Wembley Stadium on 17 or 18 April, with the official date TBC.
Saints secured their spot in the FA Cup’s final four with a comprehensive 3-0 win against second tier AFC Bournemouth on Saturday.
The Foxes defeated Manchester United 3-1 earlier this evening to get to Wembley.
Manchester City and Chelsea will play each other in the competition’s other semi-final.
The FA Cup final is set to be played at Wembley on 15 May. That game could be played in front of 20,000 fans. That game has been earmarked as one of the government’s pilot events to test the return of big crowds to UK venues.
In Southampton’s run to the semi-final, Ralph Hasenhuttl’s men have defeated Premier League competition in Wolverhampton Wanders and Arsenal - last season’s FA Cup winners.