Announcing the end of the union ban, Robin Cook, the Foreign Secretary, also signalled the beginning of talks to ensure that agreement could be reached with unions to prevent disruption at the complex.
While trade unionists will be keen to ensure that the formula is not a simple "no-strike deal" - anathema to most orthodox trade unionists - Mr Cook will be anxious to reach an accord to prevent any interruption of essential operations.
The news was greeted by prolonged cheers yesterday at the annual conference of the PTC civil service union in Blackpool, attended by some of the 14 workers who had been dismissed for refusing to give up their union membership.
As part of the impending negotiations there will also be the thorny issue of compensation for the "refuseniks", some of whom have been out of work for more than a decade. Those who stayed at the centre, but rejoined the union, are seeking recognition of the fact that they were deprived of pay increases and "fined" pounds 2,000 over two years for their recalcitrance.
In a statement, the Foreign Secretary said the decision to reintroduce trade unionism was part of the Government's commitment to "open and fair" relations at work and that it would "right a long-standing wrong".
All the refuseniks below normal retirement age will now be free to apply for jobs at the Cheltenham-based complex. Each case would be treated "sympathetically", Mr Cook said.
The Foreign Secretary declared: "GCHQ staff make a valuable contribution to protecting the liberties and freedom of our country. Today's move enables them to share fully in one of the important liberties that they defend."
John Monks, TUC general secretary, said the the ban had been a blot on Britain's reputation for democracy and human rights. "The previous government's belief that free trade unionism compromised national security was always an unjustified slur against the trade union movement and GCHQ staff in particular."
Clive Lloyd, 56, a former communications officer, said they had been expecting the announcement, but still felt overwhelmed: "Labour has kept its promise and I can't wait to walk through the gates again after spending so much time fighting to get my job back."
Baroness Thatcher, the then Prime Minister, introduced the prohibition in 1984 after civil service pay strikes spread to the centre in the early 1980s. The National Security Agency of the USA expressed concern about the industrial action and Sir Brian Tovey, director of GCHQ between 1978 and 1983, asked for the ban. Sir John Nott, who was defence secretary in 1984, said however, that the industrial action had "not in any way affected operational capability".
In his statement yesterday, Mr Cook said the present rules which outlawed industrial action would remain in place until a new deal could be completed.
"Talks with unions will begin as soon as possible to settle future arrangements for staff representation and to secure a collective agreement on no disruption to the work of GCHQ which will ensure that GCHQ's operations are protected from any threat of industrial action."
About 45 per cent of staff at GCHQ have joined the Government Communications Staff Federation, which has been refused a certificate as a bona fide union by the official Certification Officer. The federation however is now expected to merge with the PTC union.