The pair, now friends, had an intense rivalry as managers and did not speak to each other for five years after a match at Old Trafford in October 2004 ended a record 49 match unbeaten run by Arsenal. (Agencies)
"I congratulate Arsene in reaching this momentous landmark," the Scot said in a statement issued on Friday by the League Managers Association ahead of Arsenal's Premier League match at leaders Chelsea on Saturday.
"Having also reached the same milestone at one club, I cannot emphasise enough the level of dedication, resilience as well as sacrifice required and for that I have for the utmost admiration.
"Over the years we enjoyed some fantastic battles and you could say we had survived together and respected each other's efforts to play good football. I always enjoy watching Arsene's sides - Arsenal play the right way," added Ferguson.
Ferguson, who retired last year after 26 years at United, said playing against Arsenal always presented special challenges "that I burned many hours over the years thinking about.
"Perhaps the biggest compliment I could give Arsene is that I could never be anything other than competitive with my rival for 17 years," added the Scot.
"Overall this achievement once again shows what stability can bring to a football club and without doubt he has created a permanent legacy during his 1,000 matches with the club."
Wenger, who was presented with a golden cannon by the Gunners on Friday, joins Ferguson as one of just four managers to reach 1,000 games with the same club in English football.
The Frenchman is the North London club's most successful manager as well as the longest serving current boss in England.
Ferguson's comments will also be welcomed by his successor and fellow-Scot David Moyes, who has come under fire for United's poor showing in his first season in charge at Old Trafford.
Champions United are currently languishing seventh in the league, 18 points behind Chelsea. Arsenal are third, four points off the lead.
The pair, now friends, had an intense rivalry as managers and did not speak to each other for five years after a match at Old Trafford in October 2004 ended a record 49 match unbeaten run by Arsenal.