The 23-year-old, who was voted player of the year as the Terriers survived relegation from the Championship last season, is now contracted to the club until 2017.
"We want to keep our quality players and we're delighted that Alex has agreed to extend his contract at Huddersfield Town for the long term," PA quotes manager Mark Robins as saying.
"I think he can see the progression of the club on and off the field and as a local lad, who is home-grown, he has a real passion for the club and drive to add to that success.
"He has been in superb form this term and has been integral, not only to our impressive goals against record, but also in helping the team adapt to a new style of football. Alex is still a young 'keeper who will only get better with age and games, but he already has experience well beyond his years."
The England Under-19 international made his debut as a second-half substitute in a 4–1 defeat to Southend United in 2007.