Wenger arrived in north London on September 30 in 1996 and will reach the landmark figure on Saturday when his side face Chelsea.
Henry was signed as a youth player by Wenger while at Monaco and then was reunited with him when he joined the Gunners from Juventus in 1999.
"I want to wish Arsene many congratulations on this incredible achievement. I have had the privilege and honour to play under him for many years at both Monaco and Arsenal.
"To reach 1000 games for one club is a historic achievement, but not a surprising one. He is one of the very best managers in the modern game.
"I have been fortunate to play for some extremely gifted coaches. I had Pep at Barcelona and he has proved he is the best at the moment but Arsene is more than just a great manager to me because he was a father figure and a mentor.
"I will never forget his advice and guidance over the years and without him I wouldn't have achieved half the milestones in my career.
"He deserves all the accolades as he has had a huge impact on Arsenal Football Club and the lives of many players. Long may it continue."
Wenger, meanwhile, insists he is still learning his trade at Arsenal.
The 64-year-old Frenchman, appointed in late September 1996, reaches the personal landmark at Chelsea on Saturday lunchtime, when the Gunners will be out to close to within a point of the Premier League-leading Blues
Wenger, even after 17 seasons in charge of the north London club, claimed his desire to better himself burns as fierce as ever and told Arsenal Player: "You learn from every game.
"You learn more from the lost games than the games won.
"Certainly because you go into deeper analysis, you question yourself more, you question the players more and you learn basically the most from the higher the level goes up, the more you see the limitations of your team and your players.
"You learn the most in the biggest games when the pressure is there, when the talent is against you and when the pace of the game is at the top, top level. This is where you learn."
"Arsene who?" - a rare insight into Arsene Wenger by the man who brought him to English football is on Sky Sports One, Friday at 1800 & 2215 and also available On Demand.