The former Tottenham Hotspur full-back took interim charge of the Cobblers after Jimmy Floyd Hasselbaink's sacking in April and won two of his five games.
Although Austin was not able to save Northampton from the drop, several players including captain David Buchanan came out in support of the former Watford and Reading coach getting the job full-time.
"Our first priority is to try to get the club back to League One as soon as possible," Austin told the official Northampton website.
"The chairman, board, staff, players and supporters have had a glimpse at the way I want to work in the last few weeks and I have been delighted with the way everyone has responded.
"We have an important summer ahead and we have a lot of work to do."
The role is Austin's second senior managerial job, having previously taken charge of non-league Farnborough Town.