He became chairman in 1982 and presided over the appointments of George Graham and Arsene Wenger as managers and they won five league titles, five FA Cups, the League Cup and European Cup Winners' Cup between them.
Ill health forced Hill-Wood to step down from the position in June 2013.
Arsenal say he was also "instrumental" in the successful move from Highbury to Emirates Stadium in 2006.
He is survived by his wife Sally and three children Sarah, Julian and Charles.
Hill-Wood joined the Arsenal board in August 1962 and became chairman following the death of his father Denis.
With Graham as manager, between 1986 and 1995, Hill-Wood saw the Gunners win two league titles, the FA Cup, League Cup and European Cup Winners' Cup.
That was followed by success under Arsene Wenger, who was appointed in 1996, when Arsenal claimed three Premier League titles and four FA Cups. The Premier League title win in 2003/04 came on the back of an unprecedented unbeaten season for the Gunners.
Hill-Wood was succeeded by Sir Chips Keswick five years ago.
A club statement said on Friday: "Peter and his family's influence on the club cannot be understated, but at this most difficult time for his family and friends, it is Peter the man who we remember with great fondness."