The Brussels-based engineers agreed to continue working until the end of the month, when liquidators hope to be able to sell the company.
The employees, who have been working unpaid for the past week, had threatened to down tools on Friday afternoon, a move which would have closed down a quarter of Europe's internet connections.
Union representative Henrik Vermeersch said that an agreement in principle had now been reached between the workers and the company's trustees.
'Completely exhausted'
The agreement confirms that 70 employees will be paid to remain on the job for the next two weeks.
One of the engineers inside the control centre, Graham Kinsey, earlier told the BBC's World Business Report that workers are "completely exhausted" after eight days of twenty hour shifts.
Engineers have kept the KPNQwests's Ebone network running so as to avoid losing its established clients, who contribute significantly to the bankrupt company's residual value.
Mr Kinsey said customers have been loyal, with 90% still connected despite the company's problems.
It is not clear what the result of a shutdown would be, but with 25% of European internet traffic having to find a new route to its destination, some users would have problems connecting to some sites.
KPNQwest, a joint venture between Dutch telecoms giant KPN and US-based Qwest, filed for bankruptcy on 31 May after running up heavy debts to fund the construction of its fibre-optic network.