Scotland are due to play Wales in round two of the Championship at the Principality Stadium on February 12 and the match looks set to be played in front of a full house.
There were fears that Wales might move their home games to England because of the restrictions on supporters.
But Drakeford outlined the plan for returning to alert level zero during a press conference in Cardiff on Friday.
Wales has been on alert level two since Boxing Day, which has meant a limit of 50 spectators at outdoor sporting events.
From Saturday, that number will rise to 500 as part of phased lifting of restrictions following a fall in Coronavirus cases and the number of patients in critical care beds.
Further restrictions will be removed from January 21 when Wales will move to alert level zero for all outdoor activities.
Spectators will be able to return to outdoor sporting events, including the Six Nations rugby, though Covid passes will be required.
Drakeford said: “I want to thank everyone for following the rules we have had in place since Boxing Day to help keep Wales safe while the fast-moving Omicron variant has surged through our communities.
“I also want to thank everyone involved in our vaccination programme for the enormous efforts to give almost a third of the population a booster since the start of December – this has been vital in increasing our protection against Omicron.
“The actions we have taken together have helped us to weather the Omicron storm. The latest data suggests some positive signs that the peak may have passed.
“We can now look more confidently to the future and plan to start gradually removing the alert level two restrictions, starting with the outdoor measures.
“But the pandemic is not over. We will closely monitor the public health situation – this is a fast-moving and volatile variant, which could change suddenly. I urge everyone to continue to follow the rules and have your vaccines to keep Wales safe.”
Earlier this week, Scotland’s First Minister Nicola Sturgeon gave the go-ahead for full crowds to return to Scottish outdoor sporting events from Monday, January 17.
Scotland open their Six Nations campaign with a home game against England at BT Murrayfield on February 5.