Yes, there are international regulations, which shall be listed in this reply. How private entities fit in is still a disputed question. There is a lack of relevant cases, which could be used as a reference.
The "Inter-Agency Space Debris Coordination Committee" (IADC) has released the "Space Debris Mitigation Guidelines" (October 2002). If I remember it correctly, it boils down to a life-time limit in geosynchronous orbit or below of 25 years. Satellites launched in 2008 or later are required to able to be de-orbited or moved into a graveyard-orbit beyond geosynchronous orbit at the end of their life or the maximum of 25 years. The usual reference given for this statement in scientific publications is the "Space debris mitigation guidelines" of the Scientific and Technical Subcommittee of the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS), (A/AC.105/720, 1999 and A/AC.105/890, February 2007).
Some further reading: An International Environmental Agreement for space debris
mitigation among asymmetric nations, 2010.