It was confirmed last week that Siddle would be unable to fulfil his duties at Trent Bridge this year due to back and ankle injuries.
Notts have now swooped for Bird, who will be available for the first 10 games of the upcoming County Championship campaign.
"Having a bowler of international quality to spearhead our young seam attack is important for us, so we knew what type of player we wanted to go for," director of cricket Mick Newell told the club's official website.
"After Peter got injured, Jackson is the man Australia turned to. He performed very well in that Test match, he's a similar bowler to Peter in many ways and he was the obvious choice for us in the circumstances."
"Jackson is also very suitable for English conditions, particularly the types of pitches we play on at Trent Bridge."
Twenty-nine-year-old Bird has made five Test appearances for Australia, from which he has taken 21 wickets.