The fixture, which was announced on Tuesday, will mark the 125th anniversary of the Football League and is followed by a visit to Brentford and a home game with Colchester on August 17.
The Blades make the short trip for their first league meeting with Rotherham since 2005 on September 7, with the Millers making the return journey on March 8.
Christmas is spent at home with fixtures against Oldham on December 26 and Tranmere three days later while they see the new year in at Walsall on January 1.
Easter weekend sees them host Stevenage before visiting Tranmere on Easter Monday, while their campaign comes to a close with a home clash against Coventry on May 3.
- the Football League