The app will provide a trip summary, including showing on a map where any hard braking may have occurred, and then allocate good behaviour points.
Tower chief executive David Hancock said the company had no intention of using the new technology to raise premiums or reject accident claims.
"For us it is absolutely focused on incentivising drivers," he told the Herald.
"We are interested in getting people with lower risks, and rewarding them for that."
As for his own driving, he got a score of 7.5 out of 10, which would entitle him to a 10 per cent insurance discount.
Tower customer proposition general manager Mark Savage said drivers applying for discount premiums would receive a redemption code after completing their first 250km with the app.
Although they would be told what level of discount they qualified for, Mr Savage said the company did not intend publicising trigger points for each 5 per cent increment.
"We don't want people to be able to unpick it too much."
Automobile Association spokesman Mike Noon said similar road safety aids were in use overseas.
"Anything that has a road safe focus has got to be good and we want people to consider their driving style," he said last night.
Asked if the AA would have any concerns about its members' privacy, Mr Noon noted that the app was an "opt-in" tool which nobody would be compelled to use.