Delphi purchased Class A interests owned by GM for $3.8 billion. It also bought the PBGC's Class C interests for $594 million.
In a separate statement, GM said it reported a book gain of about $1.6 billion in the first quarter of 2011 related to the sale.
Delphi said it funded the transactions with cash and with $2.5 billion of new bank debt as part of a $3 billion credit facility provided by J.P. Morgan Securities LLC.
GM and U.S. pension insurer PBGC acquired stakes in Delphi as part of the supplier's emergence from bankruptcy protection in 2009. Delphi, spun off from GM in 1999, filed for Chapter 11 bankruptcy protection in 2005.
Last year, people familiar with the matter said Delphi had begun feeling out investment banks about the prospect of an initial public offering.