The Public Accounts Committee (PAC) criticised the Ministry of Defence (MoD) for failing to consult the head of the Army fully before pushing ahead with deep cuts to regular forces.
It also gave little consideration to whether it was possible for reservist numbers to be near-doubled by 2019, and it managed to squander millions of pounds through a flawed deal with Capita.
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The verdict, delivered in the cross-party committee's report on the controversial Army 2020 programme, comes as Nato leaders gather in Wales.
The scheme is intended to save more than £10 billion over a decade, by cutting 20,000 personnel from the regular army and increasing reservists to 30,000.
But the National Audit Office (NAO) has suggested that the recruitment target could take six years longer than planned to hit.
The committee said it "remained to be convinced" that the goal could be reached on time.
Chair Margaret Hodge described the handling of the project so far as "astonishing".
"The decision to reduce the size of the Army was driven by the need to make financial savings in a time of austerity," she said.
"However, it is remarkable that the chief of the general staff was not involved in all stages of the decision-making process, given the magnitude and importance of the change required, and its impact on the service.
"The MoD did not test the feasibility of recruiting and training the 30,000 reserve soldiers it needs by 2019. The strength of the Army Reserve has stayed at around 19,000 for the last two years, and we remain to be convinced that the MoD will recruit the required numbers in time.
"The Army told us that shortfalls in recruitment are increasing the risk of capability gaps emerging in some parts of the Army's structure. This in turn increases the risk of additional pressure being placed on regular troops."
Capita, the private firm brought in to handle recruitment, was said to have brought in just 2,000 reserves in 2013/14 against a target of 6,000.
The goal for recruitment of regulars was also missed by 30 per cent, according to the committee.
Yet the company was still awarded its full bonus.
Defence Secretary Michael Fallon said: "The chief of the general staff and I are confident that we will reach our target of 30,000 trained army reservists by 2018/19.
"Indeed, we have arrested the many years of decline and neglect that has plagued our reserve forces and now we need to build on that.
"Our Army 2020 plans are on track and will deliver by 2020 the army we need to counter the wide range of threats we face."