The two actors had until now been denying rumours on the possibility of their marriage happening.
Dileep, who has acted in over 130 films, has a daughter called Meenakshi through his first wife, actress Manju Warrier, who he divorced in January 2015.
Kavya Madhavan, who married Nishal Chandra in 2009, filed for divorce from him 2010 and was granted divorce in 2011.
Media reports claimed that the wedding arrangements that had been made were simple and that only close friends and family members had been invited to the event. Several celebrities from the Malayalam film industry were spotted at the wedding which took place in a hotel.