An MoD spokeswoman said later that the trust, which was given high-profile support by Diana, Princess of Wales, had asked for help with equipment. The vehicles had been used by the Army in Bosnia.
Mr Robertson told MPs that the surplus equipment - "Volvo medium-wheel tractors" - were worth about pounds 125,000 and would "considerably increase the rate of mine-clearance and the safety of operators".
He said that the Government would soon be destroying about a million anti-personnel landmines, retaining only a small number for mine-clearance and training purposes.
Since it took office, the Government has also doubled its humanitarian de-mining programme budget to pounds 10m - available to non-government organisations, and others, for mine- clearance projects.
The Halo Trust, which will use the "tractors" in northern Afghanistan, and Angola, also operates in Cambodia, Mozambique and Chechnya.
Mr Robertson said: "I am extremely proud that this government has led the way in the campaign against anti-personnel landmines. These weapons are a blight on the face of the earth, and the sooner they are outlawed forever, the safer our world will be."
The minister also said that the Government had set up a mine information and training centre, and he added: "We will continue to use the expertise of the British Army, which is formidable, to make sure that they are able to help not only other military agencies but the civil and humanitarian charitable community with the work that they are doing, to deal with a weapons system that has damaged and killed so many millions of people."