The accident happened at around 11.30am today.
Police partially closed the motorway between junctions 18 and 19, near Lockerbie.
It is not yet known if anyone was injured in the incident.
Work was underway to recover the lorries.
Traffic Scotland advised motorists to expect delays.
A Police Scotland spokeswoman said: "We received a report of an RTC involving two lorries on the M74, around two miles from Lockerbie.
"Officers are at the scene."