Wenger won three league titles during his 22-year spell in charge of the Gunners.
The Frenchman led Arsenal's "Invincibles" to an unbeaten league-winning season in 2003-04.
Ferguson and Wenger are the first two managers to be inducted into the Hall of Fame.
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The Hall of Fame launched in 2021 with David Beckham, Dennis Bergkamp, Eric Cantona, Thierry Henry, Roy Keane, Frank Lampard, Steven Gerrard and Alan Shearer the inaugural inductees.
Last year, Sergio Aguero, Didier Drogba, Vincent Kompany, Wayne Rooney, Peter Schmeichel, Paul Scholes, Patrick Vieira and Ian Wright were added.
Ferguson, who managed Manchester United from 1986 until 2013, won three league titles in a row on two separate occasions.
"It's an honour when you receive recognition like this," he said. "However, it's not just about me as a person.
"It's about the job at Manchester United and the bond we had over many years, so I'm also proud for the club, the staff and my players.
"My job was to send the fans home happy. United's history and my own expectations were the things that drove me."
Wenger, 73, arrived as one of the Premier League's first foreign managers in 1996 and won the league in his first full season at Arsenal.
"I'd like to be known as someone who loved Arsenal, who respected the values of the club and left it in a position where it can grow and become even bigger," Wenger said.
"To share this with Sir Alex is a great honour for me. It's like two boxers, you fight like mad and go the distance together.
"At the end of the day, you have respect and it will be a great opportunity to meet with him, share a good bottle of wine and memories of our old battles."
