Byrne had re-entered the field of play without the knowledge of referee Alan Lewis during the second-half of the 17-12 victory at the Liberty Stadium.
But the 2009 Lion successfully appealed against his ban and is now free to continue playing.
An Independent Appeal Committee, chaired by Rod McKenzie, found that Byrne had demonstrated that the original decision had been in error and the sanction should be varied to a fine of €5,000.
The result of the appeal means that the 29-year-old is available for selection for Wales' Six Nations opener against England on Saturday.
Wales and Lions coach Warren Gatland had delayed naming his matchday 22 for the Twickenham encounter until after Byrne's appeal had been heard in Glasgow.
Gatland will now name his side at 1pm this afternoon.