The match is to take place on 9 April 2005 at Hampden with a 3.00pm kick-off.
In the other semi, Hearts were drawn out first to play holders, Celtic.
Dundee United Director Derek Robertson said "This is an exciting draw for both clubs and, very importantly, both sets of supporters. I'm sure that both clubs feel that we have an excellent chance to progress to the final and it promises to be a great game.
We have played Hibs three times already this season, with the honours, so far, going to Hibs who have won twice to our once. However, our victory took us through to the next round of the CIS Cup, so the same again will do nicely.
The United support has been magnificent this season again and we hope that they will turn out in numbers for the semi and help us reach Hampden for the third time this year. They deserve it."