We will play the first leg at White Hart Lane in the week commencing January 19, 2015, before travelling to Bramall Lane for the second leg in the week commencing January 26, 2015.
The Blades made it through to the last four of the competition after beating Southampton 1-0 on Tuesday night.
We secured our progress with a 4-0 win at home to Newcastle United on Wednesday.
Exact dates and kick-off times for both legs of the semi-final will be confirmed in due course.
The other semi-final will be between Chelsea and Liverpool.