Speaking on Friday afternoon first minister Mark Drakeford suggested the whole of the UK would make the change at the same time – with Boris Johnson expected to address the nation on television on Sunday.
Mr Drakeford said lockdown restrictions would also be eased on garden centres and that regulations would change to allow "local authorities to begin planning how safely to reopen libraries and municipal recycling centres".
But he warned there would be no generalised lifting of the lockdown, stating: "The expert advice we have received from the chief medical office is that it is too soon to lift these restrictions, and that if we did we would see a return of the virus. The stay at home regulations much remain in place until the next review in three weeks time. We must not lose the progress that we've made."
But he said there were "some small and modest adjustment which we could make to the regulations", stating that the Welsh government wanted "to make these adjustments on Monday so that we move in step with the other nations of the United Kingdom, as part of our determined preference for a four-nation approach".
"The first [change] will be to the once a day exercise rule: the more we learn about coronavirus the evidence shows us that the risk of infection is reduced outdoors," he said.
"We will adjust our regulations to allow people to go out and exercise more than once a day but we will strengthen our regulations to make it clear that that exercise must be local. It should begin and end at home and it should not involved any significant travel away from home."
"Our second planned change to the regulations will be to allow garden centres to reopen, provided that the two metres social distancing can be applied. And thirdly we propose changing the regulations to allow local authorities to begin planning how safely to reopen libraries and municipal recycling centres."
He said the changes would apply to everyone other than the group of people being told to "shield" from the virus in their home homes and not go outside at all.