Grayson, 52, has signed a two-year contract with the Blues, replacing German Marco Pezzaiuoli at the helm.
He managed North End from February 2013 to July 2017, guiding them to promotion from League One in May 2015 via the play-off final at Wembley.
Grayson left Deepdale to take the Sunderland job ahead of the 2017/18 campaign but only lasted four months at the Stadium of Light.
Since then he has managed Bradford City, Blackpool and Fleetwood Town.
Before being in charge at North End, Grayson was manager of Blackpool, Leeds United and Huddersfield.
After his appointment was announced, Grayson told Bengaluru’s official website: “Coming to India was a possibility that I had looked into two years ago but the pandemic put all things on hold.
"When the chance came across again, I was excited to look into it. This presents a new opportunity in my football career and it is one that really excites me.
“When I spoke to the owner, his mindset was the same as mine. I want this club to be winning trophies again.
"I am aware that BFC has been very successful in the past but the last few years haven’t worked out like everybody would have liked it to.
"That happens in football – you learn from it and strive to do better – to get players to work harder on the pitch and off the pitch; that’s the exciting part for me.
"BFC have some very good young players coming through from the academy and hopefully they’ve learned from their minutes in the first team last season.
"I truly believe that they can be a massive asset to the football club, and coupled with the players who join, I think this is the perfect opportunity for me, especially because it will be a football season with the supporters.
"I’m coming not just to spend a period of time learning football in a different country. I’m coming here to win trophies at what is a fantastic football club.”