Chair John Goodfellow and Ralph Seymour-Jackson, the chief executive, will both leave the organisation, according to the Department for Business, Innovation and Skills.
It has emerged that David Willetts, the new universities minister, said he had "no confidence" in Mr Seymour-Jackson.
Mr Willetts then asked Mr Goodfellow to step down, a spokeswoman for BIS has confirmed.
A source told the Press Association that the chairman was warned he faced the sack if he did not leave of his own accord.
It comes as an audit of the SLC found students may face fresh delays again this year.
Last time, tens of thousands were left struggling to pay their bills when loans failed to arrive on time.
"Conspicuous failures" had a "far-reaching impact" on students, a report into the fiasco concluded in November.
The previous government asked accountancy firm PriceWaterhouseCooper to check up on whether the SLC was following the report's recommendations.
But on Tuesday it said there was still a "surprising lack of urgency and focus" about making changes.
The SLC is understaffed and unprepared for the deluge of applications expected over the next few months, it found.
Business Secretary Vince Cable said: "Last year's crisis in the Student Loans Company caused real upset for students and their families, many of whom lost confidence in the system. We must avoid a repetition of the problems.
"I believe a new chair and chief executive will provide the fresh leadership needed to deliver the remaining changes necessary for an improved service to customers this summer."
Mr Willetts added that "urgent changes" to the leadership were needed because "we are not out of the woods yet".
The National Union of Students welcomed the changes. President-elect Aaron Porter said the SLC had been guilty of "blundering mismanagement" last year.
"This is an opportunity for the SLC to put its previous calamitous reputation firmly behind it," he said.
He added: "We will be seeking cast-iron guarantees from the new leadership that students will never again be left without vital financial support."
Professor Sir Deian Hopkin, who wrote the initial report into the delays, will become the interim chair until ministers select a permanent replacement. The chief executive is appointed by the SLC board.
Source: http://uk.news.yahoo.com/5/20100525/
tuk-student-loans-company-bosses-forced-45dbed5.html
