The measure is meant as a relief for those who entered with a passport at a border checkpoint but are now in the country illegally and unable to work, exposing them to potentially abusive employers and conditions.
The protection will be valid up to two years and let recipients work and receive social security benefits.
Venezuelans must have entered on or before July 25 to qualify.
Migration agency director Christian Kruger said Colombia is closely watching migratory patterns ahead of Venezuela's contentious Sunday vote for a special assembly that will be tasked with rewriting constitution.
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So far no changes have been noted, but Colombia has prepared contingency plans to handle a sudden influx such as sending 1,000 officials to border points.
"Each one of them knows where to go, which team they are with," Kruger said.
The Andean neighbors have historically had a fluid border relationship, with many crossing on a daily basis to go to school or work.
More recently that tide has reversed, with many of those same migrants returning to Colombia to get away from triple- digit inflation, food and medical shortages and a homicide rate that is among the world's highest.
An estimated 25,000 Venezuelans enter Colombia daily at legal crossing points, either to buy food other supplies or to visit family. About the same number return each day, according to Colombian migration officials.
Other Andean nations including Ecuador and Peru also say they have seen an uptick in Venezuelan migrants, though the Venezuelan government denies that. Officials in Venezuela have not released migration statistics in more than a decade.
Hundreds have been lining up with suitcases in hand, she said.