The UK-based defender didn't fancy trying his luck back home, preferring to remain at Valley Parade despite having no guarantees over regular first-team action
The 26-year-old left-back has agreed a one-year extension at the League One side, where he faces competition for his stiff place from new signing Alan Sheehan.
Speaking to local newspaper the Telegraph & Argus, Meredith - who was born in WA but came through the academy at Derby County and has never played professionally in Australia - claimed he rejected approaches from the two A-League sides over concerns about the standard of the competition.
"There was interest from other clubs – there was strong interest in Australia. Melbourne Heart (City) and Western Sydney Wanderers offered me good deals, probably better," he said.
"But it wasn't right for me. I like playing in England and I like playing for Bradford.
"Maybe playing in Australia is something you do when you're a bit older and you want to go back. It's a bit slower.
"But I love the fast pace here and the competitiveness. I feel I've got unfinished business at this club."
Meredith left Derby in 2007 without making a senior appearance and has since played for Sligo Rovers, Shrewsbury Town and York City.