Ferguson was in charge at United for 26 years until 2013, overlapping with Wenger's 22-year Arsenal tenure.
The pair did not always see eye to eye on the touchline and regularly clashed as their respective teams battled for supremacy in the Premier League, particularly in the late 1990s and early 2000s.
But their fractious relationship mellowed and Ferguson hailed Wenger as one of the greats as he prepares to end a his lengthy tenure with the Gunners.
"I am really happy for Arsene Wenger," Ferguson told United's official website. "I have great respect for him and for the job he has done at Arsenal.
"It is great testament to his talent, professionalism and determination that he has been able to dedicate 22 years of his life to a job that he loves.
"In an era where football managers sometimes only last one or two seasons, it shows what an achievement it is to serve that length of time at a club the size of Arsenal.
"I am pleased that he has announced he is leaving at this stage of the season, as he can now have the send-off that he truly deserves.
"He is, without doubt, one of the greatest Premier League managers and I am proud to have been a rival, a colleague and a friend to such a great man."