Chairman Lee Power recently revealed that his search for a new boss was down to three candidates, with ex-Stevenage chief Teddy Sheringham understood to be among those in the running after being interviewed for the position.
Flitcroft is the man to have been given the nod, however, taking on his third managerial position after previous spells with Barnsley and Bury, the latter of whom sacked him in November after an 11-game winless run.
A Swindon statement read: "The club has taken its time over this appointment as it was vital after relegation that we got the right man to take the club forward and give us the best chance of promotion back to League One at the first time of asking. We are convinced David is this man.
"David has a fantastic footballing background as a player, a coach and a manager and most importantly knows this level of football and how to get out of it, having guided Bury to promotion from the Sky Bet League Two during the 2014/15 campaign.
"David has been given a very competitive budget and will now begin the job of putting a squad together with the aim of competing at the top of League Two."
Swindon finished the 2016-17 campaign 22nd in the League One standings, missing out on safety by six points.