Horne will replace Mark Skaife as Chairman, while Crompton succeeds Chris Lambden as the Independent.
Horne is best remembered for his time in American open-wheel racing during the 1980s and 90s, where he managed Jim Trueman's Truesports outfit to two titles and one Indianapolis 500 crown.
The New Zealander subsequently ran his own Tasman Motorsport outfit in the now defunct CART World Series between 1995 and 1998.
Crompton drove for Horne in the 1997 North American Touring Car Championship season, where Tasman campaigned Honda Accords.
The appointments follow confirmation from Skaife at Sandown that he would not seek re-election.
“I view this role as continuing the great work already done by Mark and the Commission,” said Horne, who eventually ran for the position unopposed, despite a push from some quarters for a return of former CEO Wayne Cattach.
“I want to provide a sounding board for key players' thoughts and ideas, to make strong and sensible decisions and bring a strategic thought process to those key decision making moments.”
Horne's V8 SuperTourer outfit currently consists of a single Ford entry that is shared by Daniel Gaunt and Andrew Waite.
With V8 Supercars' attitude towards the New Zealand class having softened dramatically since the clashes over driver movements last year, it is expected that Horne will continue in the Kiwi series.
V8 Supercars CEO James Warburton described Horne as “the ideal successor to Mark (Skaife)”.
“The role of Commission Chairman needs to be an independent, strong and robust leader,” he said.
“They need to effectively manage the Commission and its' process, make the tough decisions, broker compromise where required and be a good communicator. Steve has all of these traits.”
While Crompton's commercial ties with various aspect of the sport ensured some resistance to his appointment as the Independent, Waburton says that the former driver's knowledge will be of invaluable benefit.
“Neil has an amazing depth of knowledge of V8 Supercars which he imparts with great wisdom on and off the television screen,” said Warburton.
“I have met very few people with such an extensive understanding of the industry combined with an amazing passion.
“Neil will be a great successor to Chris who did such an outstanding job in the first two years of the Commission.”
The two-year Commission terms of Ford Performance Racing's Tim Edwards, Nissan Motorsport's Todd Kelly and Walkinshaw Racing's Steve Hallam will also expire next month, with the teams set to vote on those seats at the post-Bathurst Annual General Meeting.