The 27-year old signed with Rovers from MK Dons for £1.3million last summer when Paul Ince was in charge and has impressed the club with his performances in the past year or so.
The Republic of Ireland international said he was delighted to have been rewarded by the club.
"When I originally signed for Blackburn, the chairman was very honest with me," Andrews said.
"He said that if I nailed down a place I would get rewarded with a contract.
"I'm not going to be coming from League Two to be the top earner at the football club and the chairman was true to his word and likewise the new manager.
"The negotiations had been on-going for a few months prior to the end of last season, so they had been dragging on a little bit and I think a couple of clubs made inquiries but they were made aware that I wasn't for sale.
"I'm very happy at Blackburn, I do enjoy it there, I like living in the area so it was a no-brainer really."