The charge is part of a new dedicated pick-up and drop-off area unveiled by the airport today.
The airport said the move was to reduce congestion and improve traffic flow.
It said the current pick-up and drop-off areas would move just east of the multi-storey car park opposite the terminal.
The current free drop-off area is west of the terminal, a few minutes further away.
The Â£2 charge will allow a ten-minute stay, compared to Â£1 for five minutes at Edinburgh Airport.
Edinburgh caused a huge outcry when it introduced its charge in 2010.
Glasgow introduced pick-up fees in 2010.
Blue badge holders will continue to be given 30 minutes free parking in the short-stay car park.
The airport is also retaining its free pick-up and drop-off area in the long-stay car park, served by a five-minute shuttle bus journey.
The traffic flow on St Andrew’s Drive past the Holiday Inn Express will also be reversed in March.
Glasgow Airport managing director Amanda McMillan said: “This investment represents one of the most significant upgrades to our road network in over ten years.
"In addition, to addressing the very real issue of congestion, it will allow us to accommodate the marked increase in vehicles now using our road system and deal with recent and expected growth.
“It has been apparent for some time that our current drop-off area, which suffers from severe congestion on a daily basis, is simply no longer fit for purpose.
"It was implemented at a time when we were carrying 6.5 million passengers.
"However, we have since enjoyed sustained growth and are now fast approaching the 10 million mark.
“It is also the case that people travelling to and from the airport are wholly dependent on road access, and the current arrangements are unable to cope with such a large volume of traffic.
"It is important, therefore, that we have a safe and efficient system in place.
“I appreciate not everyone will be supportive of the new charging structure, however, we will always continue to provide a free option.
"We have resisted introducing a drop-off charge despite most airports of our size having similar arrangements in place for many years.
"However, having exhausted all possible alternatives, we have now reached a point whereby a chargeable facility is the only way to address congestion, discourage non-airport traffic and encourage best use of our road network.”
A new Â£4 million single car rental centre for all six firms will also open on 13 February beside the T2 check-in building.