The National Audit Office found significant problems with the British Army Recruiting Partnering Project because it "underestimated the complexity of the project".
The outsourcing company Capita was awarded the £495 million contract for Army recruitment in 2012, but according to the report the Army has not recruited the number of soldiers it requires in any year since the contract began.
Among the significant problems listed in the NAO report is an online recruitment system that was planned for launch in July 2013 but launched over four years late in November 2017 at a cost of £113 million - triple the original budget.
The report found that it took up to 321 days for new recruits to go from starting an application to beginning basic training and that many dropped out of the process while waiting.
Figures relate to half of the regular soldier applicants in the first six months of 2018-19.
A total of 47% of applicants dropped out of the process voluntarily in 2017-18, and both the Army and Capita believe the length of the process is a significant factor in this, the report said.
It further stated the project will not achieve its planned savings of £267 million for the Ministry of Defence.
Jeremy Lonsdale, who wrote the report said there were a "series of mistakes made in terms of implementing and managing the project".
"As a consequence, for the last six years, Capita has not met the targets for recruitment", Mr Lonsdale added.
The Commons Defence Committee was told in October that the Army currently has 77,000 fully trained troops compared with a target of 82,500.
People trying to join the Army experienced technical problems with the online recruitment system after its launch.
The Army estimates there were 13,000 fewer applications between November 2017 and March 2018 than in the same period the previous year, the report said.
This could lead to up to 1,300 fewer enlistments.
The NAO found that neither the Army nor Capita tested changes to the recruitment process before it was introduced and the number of local recruitment centres was cut from 131 to 68 to save costs.
But the Shadow Defence Secretary Nia Griffth says Ministers "can't just blame Capita" and instead they should "put their own house in order".
Ms Griffith continued: "What is happening at the moment is good public money is going down the drain.
"It's absolutly disgraceful, six years and where are we now? We're 6,000 short of where we should be in terms of Army numbers."
Capita's 10-year contract will end in 2022.
An Army Spokesperson said:
“We are fully committed to improving our recruiting process. Working with Capita we have put in place a plan to address the challenges.
“The Army has developed a range of measures to speed up the recruitment process. This includes new measures to reduce the time between applying and starting training, greater access to military role models for recruits and a new IT system.
“The Army meets all of its operational commitments to keep Britain safe.”
In response to the report, a Capita spokesperson said:
“As the NAO report states, both Capita and the Army underestimated the complexity of this project.
"Our focus is now on working with the Army to deliver a recruitment process fit for the 21st century.
"We have overhauled governance on the contract and are already seeing improvements, with applications at a five-year high and a reduction in the amount of time it takes candidates to join the Army. We are absolutely committed to getting this partnership right.”