Park and ride is what that concept is called.
Even with low parking fees and low public transport fees, you need to incentivize their usage even further by e.g. adding a city toll, so that people have to pay when going into the city by car.
But even then it's not really THE big solution. In Vienna, for example, about 450 000 cars cross city lines into the city each morning. An average parking spot in a garage is about 12.5m² plus 7.5m² of space to access it, so ~20m² in total.
That's a total of roughly 9km².
That's about 2% of the total area of Vienna, and currently it's provided by thousands of parking garages and parking lots distributed all over the city.
But if you were to build that on the outskirts of the city, the park and ride facilities would have to be enormous.
Even if you build 5-story parking towers that's still roughly 2km².