When the entry lists were released earlier this month, British No 3 Edmund, of Beverley, was three spots outside automatic qualification.
But world No 9 Gasquet, who is suffering with a back injury, has joined Juan Monaco and Australian youngster Thanasi Kokkinakis in pulling out of the year’s first grand slam, which begins on January 18.
At 102 in the rankings, Edmund thought he had done enough anyway but initially missed out owing to five players using protected rankings.
The 20-year-old came through qualifying in Melbourne last year before losing in the first round to American Steve Johnson, but gaining direct entry is a major bonus.
Edmund must have been confident he would make it because he had already signed up for the exhibition event at Kooyong, which is played at the same time as qualifying.
Edmund’s inclusion in the field shows his growing reputation, which was enhanced when he made his Davis Cup debut for Great Britain in the final against Belgium last month.
World No 16 David Goffin eventually recovered from two sets down to beat him but was given a big scare by the big-hitting Yorkshireman.
Edmund is part of an exciting generation of young players who will hope to make big strides in 2016.