The meteorological seasons are defined by the calendar months. So, literally, the passage of time defines the meteorological seasons.
Meteorological Winter: defined as December, January and February
Meteorological Spring: Defined as March, April, May
Meteorological Summer: Defined as June, July, August
Meteorological Autumn: Defined as September, October, November
The Astronomical Seasons are, as you say, defined by the solstices. the spring solstice occurs this year on March 20.