Workers had initially planned to walk out at 18:00 BST on Sunday until Wednesday morning.
But RMT general secretary Bob Crow said Metronet's "sensible" decision not to transfer jobs away to its parent company Bombardier meant the strike could now be called off.
"Our Metronet members deserve congratulating for standing solidly together to defend their organisation, jobs and conditions and to prevent further dangerous fragmentation," he said.
"Their stand, in the face of hostile media attention, has been vindicated by the outcome of this dispute."
Talks between Metronet, which is responsible for maintaining nine of the 12 tube lines, and the RMT initially broke down over the transfer of about 250 workers.
Earlier today Metronet's Mark Cooper insisted he was still hopeful a strike could be averted.
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