The Communists built the Iron Curtain to keep its people from fleeing the Soviet bloc for better lives in the West. The migration of people to the ideological enemy was humiliating and risked depleting the labor force, so they had to stop it. When the Iron Curtain fell, did lots of people from Eastern Europe and Russia suddenly start packing their bags and moving west? Or were the Communist leaders' fears unfounded?
Quite a few moved west. Immigration into the EU was 2m people in 1989 (about 50% from former Iron Curtain), and 2.1m in 1990 (the high point). Immigration gradually declined to 1.3m in 1997, and picked up again to 1.4m in 1998 (roughly half of these immigrants were from former Iron Curtain).
So, in the decade after the fall of the wall, about 8-9m people emigrated from former Iron Curtain countries to the West.