The reserve-team boss replaces Michael Appleton, who became the third managerial departure at Ewood Park this season when he was sacked following the 1-1 draw with bitter rivals Burnley.
Bowyer performed the role of caretaker following Henning Berg's dismissal in December and led the club to three wins and a draw in his four matches.
He will again be assisted by Terry McPhillips and Tony Grant.
"We will approach the situation exactly as we did previously," Bowyer told the club's official website.
"There is plenty of work to be done and we will treat the challenge very much on a game-to-game basis, starting with Blackpool on Friday.
"We will work hard and give it our best shot and all we ask is that the playing staff and the supporters get right behind the club."