Staff from the Border Force were due to take the action, in a move which would have caused major disruption to people coming into the country for the Olympics.
Home Office officials were due to ask the High Court to block the strike at Heathrow Airport one what was expected to be the busiest day of the Olympics.
The dispute was over redundancies, 8,500 job cuts and a two-year pay freeze.
But Government officials told the union last night there will be significant investment in the border force and passport service and confirmed this would mean more than 1,000 new jobs.
PCS general secretary Mark Serwotka said: "These new jobs are a welcome step towards a recognition that the Home Office has been cracking under the strain of massive job losses, and that the answer is not more cuts but more investment.
"We are pleased that with these new posts and the progress made in talks we are able to avert a strike ahead of the Olympics. But we first raised our concerns 18 months ago, so it is deeply regrettable that ministers allowed this dispute to escalate.”
PCS parliamentary group chair John McDonnell said: "Thank goodness the government has seen sense. The union has secured a tremendous breakthrough to protect its members' jobs.
"This could have been sorted weeks ago. There was no need for this heavy-handed brinkmanship by the government."