The tie was initially scheduled for Saturday evening, but postponed amid Shrewsbury's significant Covid-19 breakout.
However, the green light has now been given after Southampton's scheduled Premier League clash at Leeds next Wednesday was postponed to make way for the tie, following discussions between the FA's Professional Game Board, the Premier League, Leeds and Southampton.
Shrewsbury have not been made to forfeit their place in the competition despite being unable to fulfil the initial tie and chief executive Brian Caldwell praised the willingness of the Football Association, Premier League and Southampton for ensuring the fixture goes ahead.
More Covid tests were due to take place today, but with players who previously tested positive completing their isolation period, Shrewsbury should have enough of a team to fulfil the fixture.
Town's Sundorne Castle training facility is due to reopen with a view to recommence training tomorrow.
The tie is worth £37,500 in broadcast fees alone. A home tie against Arsenal in the fourth round on Saturday week awaits the winner.
Caldwell said: "We would like to thank the FA, Premier League and Southampton Football Club for their co-operation and willingness to reschedule the fixture.
"It did seem unfair that there was a possibility that we may have to forfeit the original tie when the circumstances around the postponement were outside of our control.
"We are therefore delighted that the FA have done all they can, in conjunction with the Premier League and Southampton, to give us the chance for the fixture to be played."