Flitcroft, 38, has been appointed until the end of the season as a permanent replacement for Keith Hill, who was sacked at the end of last month following a run of one win in 14 matches.
Flitcroft, Hill's number two at Rochdale before the pair moved to Barnsley in June 2011, had already drafted in former Fleetwood manager Micky Mellon and ex-Sunderland coach Martin Scott to help out in his first game in charge against Peterborough and they will work as his new assistants.
Bristol City's new boss Sean O'Driscoll and Inverness manager Terry Butcher both turned down the job and after Barnsley clinched back-to-back wins over Burnley and derby rivals Leeds on Saturday, the Oakwell board moved swiftly to end the growing speculation.
Rowing told Press Association Sport: "Whenever there's a managerial vacancy there's an air of uncertainty and we needed to draw a line under recent events, particularly with the way the players over the last couple of weeks had demonstrated their commitment to the club with the way they had played.
"We didn't want to lose this momentum, we wanted to get some stability back into the club and all things pointed to this conclusion, so we decided to appoint David until the end of the season."
Flitcroft, who made over 500 appearances as a midfielder for Preston, Chester, Rochdale, Macclesfield and Bury, was initially reluctant to take on the role due to his loyalty to Hill, but the players' positive response has convinced him he is the right man for the job.
"Previously David had not really shown any desire for the position,"Rowing added. "But certainly over the last few days he did and the performance of the team over the last three games clearly showed the commitment of the players towards him.
"Therefore we've given him the opportunity. We've spoken to David at length and he is totally committed to the task of keeping the club in the Championship.
"It won't be for want of hard work and commitment. There are other clubs down there and there's no reason why we can't fight our way out of trouble."
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