Parry joins his Chelsea counterpart Peter Kenyon on a 15-man board which will play a key role in running the European game over the next two years.
"It is vitally important that there is an English voice," said Parry.
Rangers director John McClelland was also elected to the group to represent Scottish football views.
The European Club Association (ECA) replaces the G14 which was a group represented by elite football clubs in Europe.
"This body has far greater credibility than G14, both with fellow clubs and European football governing body Uefa, because it was always seen as an elite group. Now we have clubs with widely diverging interests," added Parry.
In total, the ECA will have 102 members, including one from each of Europe's 53 national associations.