Cricket Australia announced Tuesday that left-arm paceman Bracken and uncapped spinner Cullen would join the team ahead of the second Test on concerns that injuries would force changes in the present team.
The Australian media have blamed the side's poor showing in Bangladesh on a tired bowling line-up and a lack of adequate preparation for the different conditions in the sub-continent after a seven-week tour of South Africa.
"Pathetic" was the one-word headline in Sydney's Daily Telegraph after Bangladesh hobbled the Australian batting order to hold them at 6-145 at stumps on day two of the first Test in Dhaka after the home side scored 427 in their first innings.
Of particular concern to Australia was the fitness of leg-spinner Shane Warne, who retired from late on day one after injuring his shoulder while throwing from the outfield.
"Our advice from team management in Bangladesh tells us there is one or two contingencies around player fitness that we may need to consider ahead of the second Test," newly appointed chairman of selectors Andrew Hilditch said.
"Due to the limited timeframe between the two Tests, there is simply not enough time to wait until the end of the first Test before making a decision.
"In this light, we have made the decision to send Nathan and Dan over earlier than expected to give them time to prepare should they be required."
Australia's showing against Bangladesh began badly with pacemen Brett Lee and Stuart Clark wicketless as the homeside poured on the runs.
The Australians also struggled against accurate seam bowling, with openers Matthew Hayden and Mike Hussey out for only six and 23 respectively and captain Ricky Ponting's wicket falling for just 21.
The tourists are now looking to Adam Gilchrist (51 not out) and the tail end to score 83 runs to avoid a humiliating follow-on.
It is the second time in a year that Bangladesh have embarrassed Australia after thrashing them in a one-day match in June in what has been labelled the biggest upset in limited overs cricket.
Columnists have blamed an overworked bowling line-up and a lack of preparation after the team's 3-0 Test series win against South Africa for the world champions' poor performance.
"Should, as now appears increasingly likely, Australia becomes the first recognised Test nation to lose to Bangladesh (which has been world cricket's whipping boy since it arrived on the scene in 2000) it has nobody to blame but itself," The Australian newspaper said.
"The fact that Cricket Australia agreed to a program that excluded practice matches and contained only two cursory training sessions in which to acclimatise to subcontinent pitches smacked of an outfit that expected to romp to victory without resistance."
Spin bowler Stuart MacGill, who earned career-best figures of 8 for 108 on day two, admitted the team was fatigued after last year's Ashes series loss in England and a hectic summer at home.
"We're tired. Not only have we been in the field for a day and a half, but I think since the Ashes started, this is our 16th Test match which has been a pretty long summer," MacGill said.