He was a pupil in Antwerp of the important genre and history painter Theodoor Rombouts under whom he started to study from 1632. He was captain of the schutterij and this may be a reason why he painted military scenes. He was friends with the flower painter Jan Philip van Thielen, who had also been a pupil of Rombouts. Van Eyck was godfather to at least one of van Thielen's nine children.
He is known for landscapes with soldiers and horsemen. A rather intriguing painting is his Scene of a rebellion (Hospitalfield Arts) depicting a rebellion in a city. It appears that a group of armed men are firing into an unarmed, unperturbed crowd. The front row of the crowd being shot at consists of three men who have their back turned towards the shooters. He also painted genre-like portraits such as the Portrait of a drinking man (sold at Van Ham).