Di Canio quit on Monday after a row with the club's owners and caretaker boss Fabrizio Piccareta also departed with a number of backroom staff after Swindon took top spot in League One with Tuesday night's 3-1 win at Tranmere.
The club's board have now turned to experienced duo Ward and Miller as they try to continue the push for promotion, despite this recent turmoil.
Midfielder Miller joined last summer from Huddersfield Town, while defender Ward sealed a permanent switch from Millwall in January and both have played around 1,000 professional games between them.
The duo's first game in charge will be Saturday's home clash against Preston North End and a goalkeeping coach and fitness coach will be brought in to assist them on a temporary basis.
An eventful week is set to continue as members of the Swindon board are meeting with the club's prospective new owners, who have backed the new management team.
A statement on the club's website read: "This initiative has the full support of the prospective new owners, allowing them the opportunity to assess all of the applications that have been received in relation to the vacant managerial position and take a considered view for the long-term benefit of the club."