The phrase 'on orders from' is correct and usable in written English.
It is used to indicate the source of an instruction or command. For example: The company assembled the new product line on orders from the president.
Many firms depend on orders from north of the Alps.
Then he walked Bonds intentionally on orders from the dugout.
Our business depends on orders from the big financial companies.
Committed to Mowbray's charge, Gloucester was mysteriously murdered, possibly on orders from Richard.
The F.B.I. said it could not discuss Mr. Muhammad on orders from the judge.
Most have cut back on orders from their suppliers to help ease their cash-flow problems.
On orders from above, truck drivers start nudging pushcarts off the street, sometimes even smashing them.
An earlier edition was destroyed on orders from an unsympathetic building manager.
Inspector Pine later said he conducted the raid on orders from superiors.
In 186 Roman magistrates, on orders from the Senate, brutally suppressed Bacchic worship in Italy.
