In the Satipatthana Sutta Buddha instructs:
Herein, monks, a monk, having gone to the forest, to the foot of a tree or to an empty place, sits down with his legs crossed, keeps his body erect and his mindfulness alert.
The ancient statues of Buddha show him sitting in this posture. An erect posture imparts the alertness of mindfulness.

In the Yoga Sutra, Patanjali describes this asana as a “steady and comfortable posture.” So, a meditative posture, besides being stable and erect must also be natural and comfortable so that it could be maintained for a long time without causing any stress or discomfort.
The condition of body in deep meditation is very similar to the condition in deep sleep. When sitting, the body may slump if not propped up properly. Crossing the legs and locking them in full-lotus position keeps the body erect even in deep meditation.
The purpose of the posture in meditation is to keep the body stably erect, even in deep meditation, in a natural and comfortable manner.
.
Niceties of Posture
In the ancient culture people were used to sitting with their legs crossed. This posture was natural and comfortable to them. So, this became the natural posture in meditation. Over time, however, other details got added that are not essential to meditation.
Zen Buddhism goes into incredible details about how to sit in meditation. It provides the size and shape of cushions to sit on, and the kinds of clothes that should be worn. It specifies how to place legs and knees on the mat, and hands and fingers in the lap. It dictates how ears should be lined up with the shoulders, and nose with the navel. It even directs the position of tip of the tongue, and the angle of the gaze. If you give importance to such niceties you can waste much time worrying about the correct posture during meditation.
Once the purpose of meditative posture is met, additional details prescribed for the posture are inessential.
.
Sitting in a Chair
In many cultures, especially in European culture, people are not used to sitting with their legs crossed. People find it easier to sit in a chair. They do not feel comfortable in the lotus posture after a while.
As long as body can be kept stably erect, there is no reason why a person cannot meditate sitting in a chair. One may use a straight-backed chair to keep the body erect. Additional cushions may be used to ensure the stability of the posture in deep meditation.

One may meditate sitting in a straight-backed chair as an alternative to the lotus position.
When meditating in a chair, it may help if the knees are parallel to the shoulders and feet are flat on the ground. The arms may rest in the lap. The hands, fingers and tongue may assume natural and relaxed positions. The eyes may be open, half open or closed according to natural tendency. The attention may focus or not focus on anything in particular. The gaze may become directed or peripheral. These variations may occur naturally during meditation.
.