Graham Lockhart, 23, and Shauna Robb, 20, from Bathgate, West Lothian, were killed in the crash along with their two children, Tyler David, aged two-and-a-half, and Arianna Rose Sheryl, aged 11 months.
The family were killed when their Fiat collided with an articulated lorry on the A801 near Polmont, on the outskirts of Falkirk, at about 2.20pm yesterday.
In a statement released through Police Scotland, relatives of Mr Lockhart said: "The Lockhart family are devastated at the loss of their son, daughter-in-law and two grandchildren, and wish to be left to grieve in peace."
Ms Robb's family released a separate statement which said: "The Robb family are devastated at the loss of their daughter, her partner and their two grandchildren, and wish to be left alone to grieve."
The family's car had crossed into the path of oncoming traffic before the crash, which happened near the Lathallan roundabout by junction four of the M9.
Police Scotland's Sergeant Andrew Thomson, from Forth Valley Road Policing, said: "We are continuing our appeal for anyone who witnessed this tragic collision or who saw a black Fiat hatchback in the area prior to the incident at 2.20pm.
"We are particularly keen to trace the driver of a silver people carrier, which was seen in the area prior to the crash."
Anyone with information is asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.