The 53-year-old was appointed at Ewood Park in late February after signing an 18-month contract but could not prevent Rovers from suffering relegation from the Sky Bet Championship on the final day of the season.
Mowbray flew out to India after the season to hold talks with the club's owners and he has committed his future after receiving assurances over plans to invest in the team.
"I enjoyed the trip to India and I'm just looking forward to the challenge of it now," said Mowbray.
"I think it's a fantastic football club, with a fantastic infrastructure. The job is to bounce back straight away and I needed some reassurances that we wouldn't be selling all of our players and that we had some budget to try and strengthen the team if we could, having lost 12 players through either loans going back or people out of contract.
"I'm looking forward to the opportunity of trying to build a team that the fans can be proud of and enjoy and hopefully we can win plenty of games. The only target is to try and bounce back at the first opportunity."
Mowbray will be tasked with guiding the club straight back into the Championship next season but he is not underestimating the difficulties of gaining promotion from League One.
"I think it's important to state from the outset that League One is a difficult league," Mowbray added.
"League One is a hard, attritional, physical league, but our aim has to be to win promotion in season one.
"I know how difficult that's going to be, because there are some pretty big teams still in League One - the likes of Charlton, Portsmouth, Wigan, Bradford etc - so there's going to be plenty of competition and we need to make sure we're at our best in every game, but the bigger goal isn't League One.
"The bigger goal is to push on past the Championship if we can. We have to first and foremost re-establish ourselves back in the Championship if we can get the job done next season and then to aim for the Premier League."
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